CoCalc Public Filesonelinersandcycles.sagewsOpen in CoCalc with one click!
Author: Sarah Wolff
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n=7 P=Permutations(n, avoiding=[2,3,1]) #P.list() Q=[] for i in [0..len(P)-1]: Q.append(P[i].to_cycles()) #turn all the avoiding oneliners into their cycle notation #print Q notcycles=[] cycles=[] for i in [0..len(Q)-1]: if len(Q[i])==1: cycles.append(Q[i]) else: notcycles.append(Q[i]) print cycles #print notcycles print len(cycles) #print len(notcycles)
print Q
[[(1, 3), (2,), (4,), (5,), (6,), (7,), (8,), (9,)], [(1, 3, 2), (4,), (5,), (6,), (7,), (8,), (9,)], [(1,), (2, 3), (4,), (5,), (6,), (7,), (8,), (9,)], [(1, 2), (3,), (4,), (5,), (6,), (7,), (8,), (9,)], [(1,), (2,), (3,), (4,), (5,), (6,), (7,), (8,), (9,)], [(1, 2), (3, 4), (5,), (6,), (7,), (8,), (9,)], [(1,), (2,), (3, 4), (5,), (6,), (7,), (8,), (9,)], [(1,), (2, 4), (3,), (5,), (6,), (7,), (8,), (9,)], [(1,), (2, 4, 3), (5,), (6,), (7,), (8,), (9,)], [(1, 4), (2, 3), (5,), (6,), (7,), (8,), (9,)], [(1, 4, 2, 3), (5,), (6,), (7,), (8,), (9,)], [(1, 4, 2), (3,), (5,), (6,), (7,), (8,), (9,)], [(1, 4, 3), (2,), (5,), (6,), (7,), (8,), (9,)], [(1, 4, 3, 2), (5,), (6,), (7,), (8,), (9,)], [(1, 3), (2,), (4, 5), (6,), (7,), (8,), (9,)], [(1, 3, 2), (4, 5), (6,), (7,), (8,), (9,)], [(1,), (2, 3), (4, 5), (6,), (7,), (8,), (9,)], [(1, 2), (3,), (4, 5), (6,), (7,), (8,), (9,)], [(1,), (2,), (3,), (4, 5), (6,), (7,), (8,), (9,)], [(1, 2), (3, 5), (4,), (6,), (7,), (8,), (9,)], [(1,), (2,), (3, 5), (4,), (6,), (7,), (8,), (9,)], [(1, 2), (3, 5, 4), (6,), (7,), (8,), (9,)], [(1,), (2,), (3, 5, 4), (6,), (7,), (8,), (9,)], [(1,), (2, 5), (3, 4), (6,), (7,), (8,), (9,)], [(1,), (2, 5, 3, 4), (6,), (7,), (8,), (9,)], [(1,), (2, 5, 3), (4,), (6,), (7,), (8,), (9,)], [(1,), (2, 5, 4), (3,), (6,), (7,), (8,), (9,)], [(1,), (2, 5, 4, 3), (6,), (7,), (8,), (9,)], [(1, 5, 4), (2, 3), (6,), (7,), (8,), (9,)], [(1, 5, 4, 2, 3), (6,), (7,), (8,), (9,)], [(1, 5, 4, 2), (3,), (6,), (7,), (8,), (9,)], [(1, 5, 4, 3), (2,), (6,), (7,), (8,), (9,)], [(1, 5, 4, 3, 2), (6,), (7,), (8,), (9,)], [(1, 5, 3), (2,), (4,), (6,), (7,), (8,), (9,)], [(1, 5, 3, 2), (4,), (6,), (7,), (8,), (9,)], [(1, 5, 2), (3, 4), (6,), (7,), (8,), (9,)], [(1, 5, 3, 4, 2), (6,), (7,), (8,), (9,)], [(1, 5), (2, 4), (3,), (6,), (7,), (8,), (9,)], [(1, 5, 2, 4), (3,), (6,), (7,), (8,), (9,)], [(1, 5, 2, 4, 3), (6,), (7,), (8,), (9,)], [(1, 5, 3, 2, 4), (6,), (7,), (8,), (9,)], [(1, 5, 3), (2, 4), (6,), (7,), (8,), (9,)], [(1, 3), (2,), (4,), (5, 6), (7,), (8,), (9,)], [(1, 3, 2), (4,), (5, 6), (7,), (8,), (9,)], [(1,), (2, 3), (4,), (5, 6), (7,), (8,), (9,)], [(1, 2), (3,), (4,), (5, 6), (7,), (8,), (9,)], [(1,), (2,), (3,), (4,), (5, 6), (7,), (8,), (9,)], [(1, 2), (3, 4), (5, 6), (7,), (8,), (9,)], [(1,), (2,), (3, 4), (5, 6), (7,), (8,), (9,)], [(1,), (2, 4), (3,), (5, 6), (7,), (8,), (9,)], [(1,), (2, 4, 3), (5, 6), (7,), (8,), (9,)], [(1, 4), (2, 3), (5, 6), (7,), (8,), (9,)], [(1, 4, 2, 3), (5, 6), (7,), (8,), (9,)], [(1, 4, 2), (3,), (5, 6), (7,), (8,), (9,)], [(1, 4, 3), (2,), (5, 6), (7,), (8,), (9,)], [(1, 4, 3, 2), (5, 6), (7,), (8,), (9,)], [(1, 3), (2,), (4, 6), (5,), (7,), (8,), (9,)], [(1, 3, 2), (4, 6), (5,), (7,), (8,), (9,)], [(1,), (2, 3), (4, 6), (5,), (7,), (8,), (9,)], [(1, 2), (3,), (4, 6), (5,), (7,), (8,), (9,)], [(1,), (2,), (3,), (4, 6), (5,), (7,), (8,), (9,)], [(1, 3), (2,), (4, 6, 5), (7,), (8,), (9,)], [(1, 3, 2), (4, 6, 5), (7,), (8,), (9,)], [(1,), (2, 3), (4, 6, 5), (7,), (8,), (9,)], [(1, 2), (3,), (4, 6, 5), (7,), (8,), (9,)], [(1,), (2,), (3,), (4, 6, 5), (7,), (8,), (9,)], [(1, 2), (3, 6), (4, 5), (7,), (8,), (9,)], [(1,), (2,), (3, 6), (4, 5), (7,), (8,), (9,)], [(1, 2), (3, 6, 4, 5), (7,), (8,), (9,)], [(1,), (2,), (3, 6, 4, 5), (7,), (8,), (9,)], [(1, 2), (3, 6, 4), (5,), (7,), (8,), (9,)], [(1,), (2,), (3, 6, 4), (5,), (7,), (8,), (9,)], [(1, 2), (3, 6, 5), (4,), (7,), (8,), (9,)], [(1,), (2,), (3, 6, 5), (4,), (7,), (8,), (9,)], [(1, 2), (3, 6, 5, 4), (7,), (8,), (9,)], [(1,), (2,), (3, 6, 5, 4), (7,), (8,), (9,)], [(1,), (2, 6, 5), (3, 4), (7,), (8,), (9,)], [(1,), (2, 6, 5, 3, 4), (7,), (8,), (9,)], [(1,), (2, 6, 5, 3), (4,), (7,), (8,), (9,)], [(1,), (2, 6, 5, 4), (3,), (7,), (8,), (9,)], [(1,), (2, 6, 5, 4, 3), (7,), (8,), (9,)], [(1,), (2, 6, 4), (3,), (5,), (7,), (8,), (9,)], [(1,), (2, 6, 4, 3), (5,), (7,), (8,), (9,)], [(1,), (2, 6, 3), (4, 5), (7,), (8,), (9,)], [(1,), (2, 6, 4, 5, 3), (7,), (8,), (9,)], [(1,), (2, 6), (3, 5), (4,), (7,), (8,), (9,)], [(1,), (2, 6, 3, 5), (4,), (7,), (8,), (9,)], [(1,), (2, 6, 3, 5, 4), (7,), (8,), (9,)], [(1,), (2, 6, 4, 3, 5), (7,), (8,), (9,)], [(1,), (2, 6, 4), (3, 5), (7,), (8,), (9,)], [(1, 6, 5, 4), (2, 3), (7,), (8,), (9,)], [(1, 6, 5, 4, 2, 3), (7,), (8,), (9,)], [(1, 6, 5, 4, 2), (3,), (7,), (8,), (9,)], [(1, 6, 5, 4, 3), (2,), (7,), (8,), (9,)], [(1, 6, 5, 4, 3, 2), (7,), (8,), (9,)], [(1, 6, 5, 3), (2,), (4,), (7,), (8,), (9,)], [(1, 6, 5, 3, 2), (4,), (7,), (8,), (9,)], [(1, 6, 5, 2), (3, 4), (7,), (8,), (9,)], [(1, 6, 5, 3, 4, 2), (7,), (8,), (9,)], [(1, 6, 5), (2, 4), (3,), (7,), (8,), (9,)], [(1, 6, 5, 2, 4), (3,), (7,), (8,), (9,)], [(1, 6, 5, 2, 4, 3), (7,), (8,), (9,)], [(1, 6, 5, 3, 2, 4), (7,), (8,), (9,)], [(1, 6, 5, 3), (2, 4), (7,), (8,), (9,)], [(1, 6, 4), (2, 3), (5,), (7,), (8,), (9,)], [(1, 6, 4, 2, 3), (5,), (7,), (8,), (9,)], [(1, 6, 4, 2), (3,), (5,), (7,), (8,), (9,)], [(1, 6, 4, 3), (2,), (5,), (7,), (8,), (9,)], [(1, 6, 4, 3, 2), (5,), (7,), (8,), (9,)], [(1, 6, 3), (2,), (4, 5), (7,), (8,), (9,)], [(1, 6, 3, 2), (4, 5), (7,), (8,), (9,)], [(1, 6, 4, 5, 3), (2,), (7,), (8,), (9,)], [(1, 6, 4, 5, 3, 2), (7,), (8,), (9,)], [(1, 6, 2), (3, 5), (4,), (7,), (8,), (9,)], [(1, 6, 3, 5, 2), (4,), (7,), (8,), (9,)], [(1, 6, 3, 5, 4, 2), (7,), (8,), (9,)], [(1, 6, 4, 3, 5, 2), (7,), (8,), (9,)], [(1, 6, 4, 2), (3, 5), (7,), (8,), (9,)], [(1, 6, 4, 2, 5), (3,), (7,), (8,), (9,)], [(1, 6, 4), (2, 5), (3,), (7,), (8,), (9,)], [(1, 6, 4, 3), (2, 5), (7,), (8,), (9,)], [(1, 6, 4), (2, 5, 3), (7,), (8,), (9,)], [(1, 6, 4, 2, 5, 3), (7,), (8,), (9,)], [(1, 6, 3, 2, 5, 4), (7,), (8,), (9,)], [(1, 6, 3), (2, 5, 4), (7,), (8,), (9,)], [(1, 6, 2, 5, 3), (4,), (7,), (8,), (9,)], [(1, 6, 3), (2, 5), (4,), (7,), (8,), (9,)], [(1, 6), (2, 5), (3, 4), (7,), (8,), (9,)], [(1, 6, 2, 5), (3, 4), (7,), (8,), (9,)], [(1, 6, 2, 5, 3, 4), (7,), (8,), (9,)], [(1, 6, 3, 4, 2, 5), (7,), (8,), (9,)], [(1, 6, 3, 4), (2, 5), (7,), (8,), (9,)], [(1, 3), (2,), (4,), (5,), (6, 7), (8,), (9,)], [(1, 3, 2), (4,), (5,), (6, 7), (8,), (9,)], [(1,), (2, 3), (4,), (5,), (6, 7), (8,), (9,)], [(1, 2), (3,), (4,), (5,), (6, 7), (8,), (9,)], [(1,), (2,), (3,), (4,), (5,), (6, 7), (8,), (9,)], [(1, 2), (3, 4), (5,), (6, 7), (8,), (9,)], [(1,), (2,), (3, 4), (5,), (6, 7), (8,), (9,)], [(1,), (2, 4), (3,), (5,), (6, 7), (8,), (9,)], [(1,), (2, 4, 3), (5,), (6, 7), (8,), (9,)], [(1, 4), (2, 3), (5,), (6, 7), (8,), (9,)], [(1, 4, 2, 3), (5,), (6, 7), (8,), (9,)], [(1, 4, 2), (3,), (5,), (6, 7), (8,), (9,)], [(1, 4, 3), (2,), (5,), (6, 7), (8,), (9,)], [(1, 4, 3, 2), (5,), (6, 7), (8,), (9,)], [(1, 3), (2,), (4, 5), (6, 7), (8,), (9,)], [(1, 3, 2), (4, 5), (6, 7), (8,), (9,)], [(1,), (2, 3), (4, 5), (6, 7), (8,), (9,)], [(1, 2), (3,), (4, 5), (6, 7), (8,), (9,)], [(1,), (2,), (3,), (4, 5), (6, 7), (8,), (9,)], [(1, 2), (3, 5), (4,), (6, 7), (8,), (9,)], [(1,), (2,), (3, 5), (4,), (6, 7), (8,), (9,)], [(1, 2), (3, 5, 4), (6, 7), (8,), (9,)], [(1,), (2,), (3, 5, 4), (6, 7), (8,), (9,)], [(1,), (2, 5), (3, 4), (6, 7), (8,), (9,)], [(1,), (2, 5, 3, 4), (6, 7), (8,), (9,)], [(1,), (2, 5, 3), (4,), (6, 7), (8,), (9,)], [(1,), (2, 5, 4), (3,), (6, 7), (8,), (9,)], [(1,), (2, 5, 4, 3), (6, 7), (8,), (9,)], [(1, 5, 4), (2, 3), (6, 7), (8,), (9,)], [(1, 5, 4, 2, 3), (6, 7), (8,), (9,)], [(1, 5, 4, 2), (3,), (6, 7), (8,), (9,)], [(1, 5, 4, 3), (2,), (6, 7), (8,), (9,)], [(1, 5, 4, 3, 2), (6, 7), (8,), (9,)], [(1, 5, 3), (2,), (4,), (6, 7), (8,), (9,)], [(1, 5, 3, 2), (4,), (6, 7), (8,), (9,)], [(1, 5, 2), (3, 4), (6, 7), (8,), (9,)], [(1, 5, 3, 4, 2), (6, 7), (8,), (9,)], [(1, 5), (2, 4), (3,), (6, 7), (8,), (9,)], [(1, 5, 2, 4), (3,), (6, 7), (8,), (9,)], [(1, 5, 2, 4, 3), (6, 7), (8,), (9,)], [(1, 5, 3, 2, 4), (6, 7), (8,), (9,)], [(1, 5, 3), (2, 4), (6, 7), (8,), (9,)], [(1, 3), (2,), (4,), (5, 7), (6,), (8,), (9,)], [(1, 3, 2), (4,), (5, 7), (6,), (8,), (9,)], [(1,), (2, 3), (4,), (5, 7), (6,), (8,), (9,)], [(1, 2), (3,), (4,), (5, 7), (6,), (8,), (9,)], [(1,), (2,), (3,), (4,), (5, 7), (6,), (8,), (9,)], [(1, 2), (3, 4), (5, 7), (6,), (8,), (9,)], [(1,), (2,), (3, 4), (5, 7), (6,), (8,), (9,)], [(1,), (2, 4), (3,), (5, 7), (6,), (8,), (9,)], [(1,), (2, 4, 3), (5, 7), (6,), (8,), (9,)], [(1, 4), (2, 3), (5, 7), (6,), (8,), (9,)], [(1, 4, 2, 3), (5, 7), (6,), (8,), (9,)], [(1, 4, 2), (3,), (5, 7), (6,), (8,), (9,)], [(1, 4, 3), (2,), (5, 7), (6,), (8,), (9,)], [(1, 4, 3, 2), (5, 7), (6,), (8,), (9,)], [(1, 3), (2,), (4,), (5, 7, 6), (8,), (9,)], [(1, 3, 2), (4,), (5, 7, 6), (8,), (9,)], [(1,), (2, 3), (4,), (5, 7, 6), (8,), (9,)], [(1, 2), (3,), (4,), (5, 7, 6), (8,), (9,)], [(1,), (2,), (3,), (4,), (5, 7, 6), (8,), (9,)], [(1, 2), (3, 4), (5, 7, 6), (8,), (9,)], [(1,), (2,), (3, 4), (5, 7, 6), (8,), (9,)], [(1,), (2, 4), (3,), (5, 7, 6), (8,), (9,)], [(1,), (2, 4, 3), (5, 7, 6), (8,), (9,)], [(1, 4), (2, 3), (5, 7, 6), (8,), (9,)], [(1, 4, 2, 3), (5, 7, 6), (8,), (9,)], [(1, 4, 2), (3,), (5, 7, 6), (8,), (9,)], [(1, 4, 3), (2,), (5, 7, 6), (8,), (9,)], [(1, 4, 3, 2), (5, 7, 6), (8,), (9,)], [(1, 3), (2,), (4, 7), (5, 6), (8,), (9,)], [(1, 3, 2), (4, 7), (5, 6), (8,), (9,)], [(1,), (2, 3), (4, 7), (5, 6), (8,), (9,)], [(1, 2), (3,), (4, 7), (5, 6), (8,), (9,)], [(1,), (2,), (3,), (4, 7), (5, 6), (8,), (9,)], [(1, 3), (2,), (4, 7, 5, 6), (8,), (9,)], [(1, 3, 2), (4, 7, 5, 6), (8,), (9,)], [(1,), (2, 3), (4, 7, 5, 6), (8,), (9,)], [(1, 2), (3,), (4, 7, 5, 6), (8,), (9,)], [(1,), (2,), (3,), (4, 7, 5, 6), (8,), (9,)], [(1, 3), (2,), (4, 7, 5), (6,), (8,), (9,)], [(1, 3, 2), (4, 7, 5), (6,), (8,), (9,)], [(1,), (2, 3), (4, 7, 5), (6,), (8,), (9,)], [(1, 2), (3,), (4, 7, 5), (6,), (8,), (9,)], [(1,), (2,), (3,), (4, 7, 5), (6,), (8,), (9,)], [(1, 3), (2,), (4, 7, 6), (5,), (8,), (9,)], [(1, 3, 2), (4, 7, 6), (5,), (8,), (9,)], [(1,), (2, 3), (4, 7, 6), (5,), (8,), (9,)], [(1, 2), (3,), (4, 7, 6), (5,), (8,), (9,)], [(1,), (2,), (3,), (4, 7, 6), (5,), (8,), (9,)], [(1, 3), (2,), (4, 7, 6, 5), (8,), (9,)], [(1, 3, 2), (4, 7, 6, 5), (8,), (9,)], [(1,), (2, 3), (4, 7, 6, 5), (8,), (9,)], [(1, 2), (3,), (4, 7, 6, 5), (8,), (9,)], [(1,), (2,), (3,), (4, 7, 6, 5), (8,), (9,)], [(1, 2), (3, 7, 6), (4, 5), (8,), (9,)], [(1,), (2,), (3, 7, 6), (4, 5), (8,), (9,)], [(1, 2), (3, 7, 6, 4, 5), (8,), (9,)], [(1,), (2,), (3, 7, 6, 4, 5), (8,), (9,)], [(1, 2), (3, 7, 6, 4), (5,), (8,), (9,)], [(1,), (2,), (3, 7, 6, 4), (5,), (8,), (9,)], [(1, 2), (3, 7, 6, 5), (4,), (8,), (9,)], [(1,), (2,), (3, 7, 6, 5), (4,), (8,), (9,)], [(1, 2), (3, 7, 6, 5, 4), (8,), (9,)], [(1,), (2,), (3, 7, 6, 5, 4), (8,), (9,)], [(1, 2), (3, 7, 5), (4,), (6,), (8,), (9,)], [(1,), (2,), (3, 7, 5), (4,), (6,), (8,), (9,)], [(1, 2), (3, 7, 5, 4), (6,), (8,), (9,)], [(1,), (2,), (3, 7, 5, 4), (6,), (8,), (9,)], [(1, 2), (3, 7, 4), (5, 6), (8,), (9,)], [(1,), (2,), (3, 7, 4), (5, 6), (8,), (9,)], [(1, 2), (3, 7, 5, 6, 4), (8,), (9,)], [(1,), (2,), (3, 7, 5, 6, 4), (8,), (9,)], [(1, 2), (3, 7), (4, 6), (5,), (8,), (9,)], [(1,), (2,), (3, 7), (4, 6), (5,), (8,), (9,)], [(1, 2), (3, 7, 4, 6), (5,), (8,), (9,)], [(1,), (2,), (3, 7, 4, 6), (5,), (8,), (9,)], [(1, 2), (3, 7, 4, 6, 5), (8,), (9,)], [(1,), (2,), (3, 7, 4, 6, 5), (8,), (9,)], [(1, 2), (3, 7, 5, 4, 6), (8,), (9,)], [(1,), (2,), (3, 7, 5, 4, 6), (8,), (9,)], [(1, 2), (3, 7, 5), (4, 6), (8,), (9,)], [(1,), (2,), (3, 7, 5), (4, 6), (8,), (9,)], [(1,), (2, 7, 6, 5), (3, 4), (8,), (9,)], [(1,), (2, 7, 6, 5, 3, 4), (8,), (9,)], [(1,), (2, 7, 6, 5, 3), (4,), (8,), (9,)], [(1,), (2, 7, 6, 5, 4), (3,), (8,), (9,)], [(1,), (2, 7, 6, 5, 4, 3), (8,), (9,)], [(1,), (2, 7, 6, 4), (3,), (5,), (8,), (9,)], [(1,), (2, 7, 6, 4, 3), (5,), (8,), (9,)], [(1,), (2, 7, 6, 3), (4, 5), (8,), (9,)], [(1,), (2, 7, 6, 4, 5, 3), (8,), (9,)], [(1,), (2, 7, 6), (3, 5), (4,), (8,), (9,)], [(1,), (2, 7, 6, 3, 5), (4,), (8,), (9,)], [(1,), (2, 7, 6, 3, 5, 4), (8,), (9,)], [(1,), (2, 7, 6, 4, 3, 5), (8,), (9,)], [(1,), (2, 7, 6, 4), (3, 5), (8,), (9,)], [(1,), (2, 7, 5), (3, 4), (6,), (8,), (9,)], [(1,), (2, 7, 5, 3, 4), (6,), (8,), (9,)], [(1,), (2, 7, 5, 3), (4,), (6,), (8,), (9,)], [(1,), (2, 7, 5, 4), (3,), (6,), (8,), (9,)], [(1,), (2, 7, 5, 4, 3), (6,), (8,), (9,)], [(1,), (2, 7, 4), (3,), (5, 6), (8,), (9,)], [(1,), (2, 7, 4, 3), (5, 6), (8,), (9,)], [(1,), (2, 7, 5, 6, 4), (3,), (8,), (9,)], [(1,), (2, 7, 5, 6, 4, 3), (8,), (9,)], [(1,), (2, 7, 3), (4, 6), (5,), (8,), (9,)], [(1,), (2, 7, 4, 6, 3), (5,), (8,), (9,)], [(1,), (2, 7, 4, 6, 5, 3), (8,), (9,)], [(1,), (2, 7, 5, 4, 6, 3), (8,), (9,)], [(1,), (2, 7, 5, 3), (4, 6), (8,), (9,)], [(1,), (2, 7, 5, 3, 6), (4,), (8,), (9,)], [(1,), (2, 7, 5), (3, 6), (4,), (8,), (9,)], [(1,), (2, 7, 5, 4), (3, 6), (8,), (9,)], [(1,), (2, 7, 5), (3, 6, 4), (8,), (9,)], [(1,), (2, 7, 5, 3, 6, 4), (8,), (9,)], [(1,), (2, 7, 4, 3, 6, 5), (8,), (9,)], [(1,), (2, 7, 4), (3, 6, 5), (8,), (9,)], [(1,), (2, 7, 3, 6, 4), (5,), (8,), (9,)], [(1,), (2, 7, 4), (3, 6), (5,), (8,), (9,)], [(1,), (2, 7), (3, 6), (4, 5), (8,), (9,)], [(1,), (2, 7, 3, 6), (4, 5), (8,), (9,)], [(1,), (2, 7, 3, 6, 4, 5), (8,), (9,)], [(1,), (2, 7, 4, 5, 3, 6), (8,), (9,)], [(1,), (2, 7, 4, 5), (3, 6), (8,), (9,)], [(1, 7, 6, 5, 4), (2, 3), (8,), (9,)], [(1, 7, 6, 5, 4, 2, 3), (8,), (9,)], [(1, 7, 6, 5, 4, 2), (3,), (8,), (9,)], [(1, 7, 6, 5, 4, 3), (2,), (8,), (9,)], [(1, 7, 6, 5, 4, 3, 2), (8,), (9,)], [(1, 7, 6, 5, 3), (2,), (4,), (8,), (9,)], [(1, 7, 6, 5, 3, 2), (4,), (8,), (9,)], [(1, 7, 6, 5, 2), (3, 4), (8,), (9,)], [(1, 7, 6, 5, 3, 4, 2), (8,), (9,)], [(1, 7, 6, 5), (2, 4), (3,), (8,), (9,)], [(1, 7, 6, 5, 2, 4), (3,), (8,), (9,)], [(1, 7, 6, 5, 2, 4, 3), (8,), (9,)], [(1, 7, 6, 5, 3, 2, 4), (8,), (9,)], [(1, 7, 6, 5, 3), (2, 4), (8,), (9,)], [(1, 7, 6, 4), (2, 3), (5,), (8,), (9,)], [(1, 7, 6, 4, 2, 3), (5,), (8,), (9,)], [(1, 7, 6, 4, 2), (3,), (5,), (8,), (9,)], [(1, 7, 6, 4, 3), (2,), (5,), (8,), (9,)], [(1, 7, 6, 4, 3, 2), (5,), (8,), (9,)], [(1, 7, 6, 3), (2,), (4, 5), (8,), (9,)], [(1, 7, 6, 3, 2), (4, 5), (8,), (9,)], [(1, 7, 6, 4, 5, 3), (2,), (8,), (9,)], [(1, 7, 6, 4, 5, 3, 2), (8,), (9,)], [(1, 7, 6, 2), (3, 5), (4,), (8,), (9,)], [(1, 7, 6, 3, 5, 2), (4,), (8,), (9,)], [(1, 7, 6, 3, 5, 4, 2), (8,), (9,)], [(1, 7, 6, 4, 3, 5, 2), (8,), (9,)], [(1, 7, 6, 4, 2), (3, 5), (8,), (9,)], [(1, 7, 6, 4, 2, 5), (3,), (8,), (9,)], [(1, 7, 6, 4), (2, 5), (3,), (8,), (9,)], [(1, 7, 6, 4, 3), (2, 5), (8,), (9,)], [(1, 7, 6, 4), (2, 5, 3), (8,), (9,)], [(1, 7, 6, 4, 2, 5, 3), (8,), (9,)], [(1, 7, 6, 3, 2, 5, 4), (8,), (9,)], [(1, 7, 6, 3), (2, 5, 4), (8,), (9,)], [(1, 7, 6, 2, 5, 3), (4,), (8,), (9,)], [(1, 7, 6, 3), (2, 5), (4,), (8,), (9,)], [(1, 7, 6), (2, 5), (3, 4), (8,), (9,)], [(1, 7, 6, 2, 5), (3, 4), (8,), (9,)], [(1, 7, 6, 2, 5, 3, 4), (8,), (9,)], [(1, 7, 6, 3, 4, 2, 5), (8,), (9,)], [(1, 7, 6, 3, 4), (2, 5), (8,), (9,)], [(1, 7, 5, 4), (2, 3), (6,), (8,), (9,)], [(1, 7, 5, 4, 2, 3), (6,), (8,), (9,)], [(1, 7, 5, 4, 2), (3,), (6,), (8,), (9,)], [(1, 7, 5, 4, 3), (2,), (6,), (8,), (9,)], [(1, 7, 5, 4, 3, 2), (6,), (8,), (9,)], [(1, 7, 5, 3), (2,), (4,), (6,), (8,), (9,)], [(1, 7, 5, 3, 2), (4,), (6,), (8,), (9,)], [(1, 7, 5, 2), (3, 4), (6,), (8,), (9,)], [(1, 7, 5, 3, 4, 2), (6,), (8,), (9,)], [(1, 7, 5), (2, 4), (3,), (6,), (8,), (9,)], [(1, 7, 5, 2, 4), (3,), (6,), (8,), (9,)], [(1, 7, 5, 2, 4, 3), (6,), (8,), (9,)], [(1, 7, 5, 3, 2, 4), (6,), (8,), (9,)], [(1, 7, 5, 3), (2, 4), (6,), (8,), (9,)], [(1, 7, 4), (2, 3), (5, 6), (8,), (9,)], [(1, 7, 4, 2, 3), (5, 6), (8,), (9,)], [(1, 7, 4, 2), (3,), (5, 6), (8,), (9,)], [(1, 7, 4, 3), (2,), (5, 6), (8,), (9,)], [(1, 7, 4, 3, 2), (5, 6), (8,), (9,)], [(1, 7, 5, 6, 4), (2, 3), (8,), (9,)], [(1, 7, 5, 6, 4, 2, 3), (8,), (9,)], [(1, 7, 5, 6, 4, 2), (3,), (8,), (9,)], [(1, 7, 5, 6, 4, 3), (2,), (8,), (9,)], [(1, 7, 5, 6, 4, 3, 2), (8,), (9,)], [(1, 7, 3), (2,), (4, 6), (5,), (8,), (9,)], [(1, 7, 3, 2), (4, 6), (5,), (8,), (9,)], [(1, 7, 4, 6, 3), (2,), (5,), (8,), (9,)], [(1, 7, 4, 6, 3, 2), (5,), (8,), (9,)], [(1, 7, 4, 6, 5, 3), (2,), (8,), (9,)], [(1, 7, 4, 6, 5, 3, 2), (8,), (9,)], [(1, 7, 5, 4, 6, 3), (2,), (8,), (9,)], [(1, 7, 5, 4, 6, 3, 2), (8,), (9,)], [(1, 7, 5, 3), (2,), (4, 6), (8,), (9,)], [(1, 7, 5, 3, 2), (4, 6), (8,), (9,)], [(1, 7, 5, 3, 6, 2), (4,), (8,), (9,)], [(1, 7, 5, 2), (3, 6), (4,), (8,), (9,)], [(1, 7, 5, 4, 2), (3, 6), (8,), (9,)], [(1, 7, 5, 2), (3, 6, 4), (8,), (9,)], [(1, 7, 5, 3, 6, 4, 2), (8,), (9,)], [(1, 7, 4, 3, 6, 5, 2), (8,), (9,)], [(1, 7, 4, 2), (3, 6, 5), (8,), (9,)], [(1, 7, 3, 6, 4, 2), (5,), (8,), (9,)], [(1, 7, 4, 2), (3, 6), (5,), (8,), (9,)], [(1, 7, 2), (3, 6), (4, 5), (8,), (9,)], [(1, 7, 3, 6, 2), (4, 5), (8,), (9,)], [(1, 7, 3, 6, 4, 5, 2), (8,), (9,)], [(1, 7, 4, 5, 3, 6, 2), (8,), (9,)], [(1, 7, 4, 5, 2), (3, 6), (8,), (9,)], [(1, 7, 5), (2, 6, 4), (3,), (8,), (9,)], [(1, 7, 5, 2, 6, 4), (3,), (8,), (9,)], [(1, 7, 5, 2, 6, 4, 3), (8,), (9,)], [(1, 7, 5, 3, 2, 6, 4), (8,), (9,)], [(1, 7, 5, 3), (2, 6, 4), (8,), (9,)], [(1, 7, 5, 4), (2, 6, 3), (8,), (9,)], [(1, 7, 5, 4, 2, 6, 3), (8,), (9,)], [(1, 7, 5, 3), (2, 6), (4,), (8,), (9,)], [(1, 7, 5, 2, 6, 3), (4,), (8,), (9,)], [(1, 7, 5, 2, 6), (3, 4), (8,), (9,)], [(1, 7, 5), (2, 6), (3, 4), (8,), (9,)], [(1, 7, 5, 3, 4), (2, 6), (8,), (9,)], [(1, 7, 5), (2, 6, 3, 4), (8,), (9,)], [(1, 7, 5, 2, 6, 3, 4), (8,), (9,)], [(1, 7, 4, 2, 6, 5), (3,), (8,), (9,)], [(1, 7, 4), (2, 6, 5), (3,), (8,), (9,)], [(1, 7, 4, 3), (2, 6, 5), (8,), (9,)], [(1, 7, 4), (2, 6, 5, 3), (8,), (9,)], [(1, 7, 4, 2, 6, 5, 3), (8,), (9,)], [(1, 7, 3, 2, 6, 4), (5,), (8,), (9,)], [(1, 7, 3), (2, 6, 4), (5,), (8,), (9,)], [(1, 7, 4), (2, 6, 3), (5,), (8,), (9,)], [(1, 7, 4, 2, 6, 3), (5,), (8,), (9,)], [(1, 7, 2, 6, 3), (4, 5), (8,), (9,)], [(1, 7, 3), (2, 6), (4, 5), (8,), (9,)], [(1, 7, 3), (2, 6, 4, 5), (8,), (9,)], [(1, 7, 4, 5, 3), (2, 6), (8,), (9,)], [(1, 7, 4, 5, 2, 6, 3), (8,), (9,)], [(1, 7, 4, 3, 5, 2, 6), (8,), (9,)], [(1, 7, 4, 3, 5), (2, 6), (8,), (9,)], [(1, 7, 4), (2, 6), (3, 5), (8,), (9,)], [(1, 7, 4, 2, 6, 3, 5), (8,), (9,)], [(1, 7, 4), (2, 6, 3, 5), (8,), (9,)], [(1, 7, 3, 5), (2, 6, 4), (8,), (9,)], [(1, 7, 3, 5, 2, 6, 4), (8,), (9,)], [(1, 7, 2, 6, 3, 5, 4), (8,), (9,)], [(1, 7, 3, 5, 4), (2, 6), (8,), (9,)], [(1, 7), (2, 6), (3, 5), (4,), (8,), (9,)], [(1, 7, 2, 6), (3, 5), (4,), (8,), (9,)], [(1, 7, 2, 6, 3, 5), (4,), (8,), (9,)], [(1, 7, 3, 5, 2, 6), (4,), (8,), (9,)], [(1, 7, 3, 5), (2, 6), (4,), (8,), (9,)], [(1, 3), (2,), (4,), (5,), (6,), (7, 8), (9,)], [(1, 3, 2), (4,), (5,), (6,), (7, 8), (9,)], [(1,), (2, 3), (4,), (5,), (6,), (7, 8), (9,)], [(1, 2), (3,), (4,), (5,), (6,), (7, 8), (9,)], [(1,), (2,), (3,), (4,), (5,), (6,), (7, 8), (9,)], [(1, 2), (3, 4), (5,), (6,), (7, 8), (9,)], [(1,), (2,), (3, 4), (5,), (6,), (7, 8), (9,)], [(1,), (2, 4), (3,), (5,), (6,), (7, 8), (9,)], [(1,), (2, 4, 3), (5,), (6,), (7, 8), (9,)], [(1, 4), (2, 3), (5,), (6,), (7, 8), (9,)], [(1, 4, 2, 3), (5,), (6,), (7, 8), (9,)], [(1, 4, 2), (3,), (5,), (6,), (7, 8), (9,)], [(1, 4, 3), (2,), (5,), (6,), (7, 8), (9,)], [(1, 4, 3, 2), (5,), (6,), (7, 8), (9,)], [(1, 3), (2,), (4, 5), (6,), (7, 8), (9,)], [(1, 3, 2), (4, 5), (6,), (7, 8), (9,)], [(1,), (2, 3), (4, 5), (6,), (7, 8), (9,)], [(1, 2), (3,), (4, 5), (6,), (7, 8), (9,)], [(1,), (2,), (3,), (4, 5), (6,), (7, 8), (9,)], [(1, 2), (3, 5), (4,), (6,), (7, 8), (9,)], [(1,), (2,), (3, 5), (4,), (6,), (7, 8), (9,)], [(1, 2), (3, 5, 4), (6,), (7, 8), (9,)], [(1,), (2,), (3, 5, 4), (6,), (7, 8), (9,)], [(1,), (2, 5), (3, 4), (6,), (7, 8), (9,)], [(1,), (2, 5, 3, 4), (6,), (7, 8), (9,)], [(1,), (2, 5, 3), (4,), (6,), (7, 8), (9,)], [(1,), (2, 5, 4), (3,), (6,), (7, 8), (9,)], [(1,), (2, 5, 4, 3), (6,), (7, 8), (9,)], [(1, 5, 4), (2, 3), (6,), (7, 8), (9,)], [(1, 5, 4, 2, 3), (6,), (7, 8), (9,)], [(1, 5, 4, 2), (3,), (6,), (7, 8), (9,)], [(1, 5, 4, 3), (2,), (6,), (7, 8), (9,)], [(1, 5, 4, 3, 2), (6,), (7, 8), (9,)], [(1, 5, 3), (2,), (4,), (6,), (7, 8), (9,)], [(1, 5, 3, 2), (4,), (6,), (7, 8), (9,)], [(1, 5, 2), (3, 4), (6,), (7, 8), (9,)], [(1, 5, 3, 4, 2), (6,), (7, 8), (9,)], [(1, 5), (2, 4), (3,), (6,), (7, 8), (9,)], [(1, 5, 2, 4), (3,), (6,), (7, 8), (9,)], [(1, 5, 2, 4, 3), (6,), (7, 8), (9,)], [(1, 5, 3, 2, 4), (6,), (7, 8), (9,)], [(1, 5, 3), (2, 4), (6,), (7, 8), (9,)], [(1, 3), (2,), (4,), (5, 6), (7, 8), (9,)], [(1, 3, 2), (4,), (5, 6), (7, 8), (9,)], [(1,), (2, 3), (4,), (5, 6), (7, 8), (9,)], [(1, 2), (3,), (4,), (5, 6), (7, 8), (9,)], [(1,), (2,), (3,), (4,), (5, 6), (7, 8), (9,)], [(1, 2), (3, 4), (5, 6), (7, 8), (9,)], [(1,), (2,), (3, 4), (5, 6), (7, 8), (9,)], [(1,), (2, 4), (3,), (5, 6), (7, 8), (9,)], [(1,), (2, 4, 3), (5, 6), (7, 8), (9,)], [(1, 4), (2, 3), (5, 6), (7, 8), (9,)], [(1, 4, 2, 3), (5, 6), (7, 8), (9,)], [(1, 4, 2), (3,), (5, 6), (7, 8), (9,)], [(1, 4, 3), (2,), (5, 6), (7, 8), (9,)], [(1, 4, 3, 2), (5, 6), (7, 8), (9,)], [(1, 3), (2,), (4, 6), (5,), (7, 8), (9,)], [(1, 3, 2), (4, 6), (5,), (7, 8), (9,)], [(1,), (2, 3), (4, 6), (5,), (7, 8), (9,)], [(1, 2), (3,), (4, 6), (5,), (7, 8), (9,)], [(1,), (2,), (3,), (4, 6), (5,), (7, 8), (9,)], [(1, 3), (2,), (4, 6, 5), (7, 8), (9,)], [(1, 3, 2), (4, 6, 5), (7, 8), (9,)], [(1,), (2, 3), (4, 6, 5), (7, 8), (9,)], [(1, 2), (3,), (4, 6, 5), (7, 8), (9,)], [(1,), (2,), (3,), (4, 6, 5), (7, 8), (9,)], [(1, 2), (3, 6), (4, 5), (7, 8), (9,)], [(1,), (2,), (3, 6), (4, 5), (7, 8), (9,)], [(1, 2), (3, 6, 4, 5), (7, 8), (9,)], [(1,), (2,), (3, 6, 4, 5), (7, 8), (9,)], [(1, 2), (3, 6, 4), (5,), (7, 8), (9,)], [(1,), (2,), (3, 6, 4), (5,), (7, 8), (9,)], [(1, 2), (3, 6, 5), (4,), (7, 8), (9,)], [(1,), (2,), (3, 6, 5), (4,), (7, 8), (9,)], [(1, 2), (3, 6, 5, 4), (7, 8), (9,)], [(1,), (2,), (3, 6, 5, 4), (7, 8), (9,)], [(1,), (2, 6, 5), (3, 4), (7, 8), (9,)], [(1,), (2, 6, 5, 3, 4), (7, 8), (9,)], [(1,), (2, 6, 5, 3), (4,), (7, 8), (9,)], [(1,), (2, 6, 5, 4), (3,), (7, 8), (9,)], [(1,), (2, 6, 5, 4, 3), (7, 8), (9,)], [(1,), (2, 6, 4), (3,), (5,), (7, 8), (9,)], [(1,), (2, 6, 4, 3), (5,), (7, 8), (9,)], [(1,), (2, 6, 3), (4, 5), (7, 8), (9,)], [(1,), (2, 6, 4, 5, 3), (7, 8), (9,)], [(1,), (2, 6), (3, 5), (4,), (7, 8), (9,)], [(1,), (2, 6, 3, 5), (4,), (7, 8), (9,)], [(1,), (2, 6, 3, 5, 4), (7, 8), (9,)], [(1,), (2, 6, 4, 3, 5), (7, 8), (9,)], [(1,), (2, 6, 4), (3, 5), (7, 8), (9,)], [(1, 6, 5, 4), (2, 3), (7, 8), (9,)], [(1, 6, 5, 4, 2, 3), (7, 8), (9,)], [(1, 6, 5, 4, 2), (3,), (7, 8), (9,)], [(1, 6, 5, 4, 3), (2,), (7, 8), (9,)], [(1, 6, 5, 4, 3, 2), (7, 8), (9,)], [(1, 6, 5, 3), (2,), (4,), (7, 8), (9,)], [(1, 6, 5, 3, 2), (4,), (7, 8), (9,)], [(1, 6, 5, 2), (3, 4), (7, 8), (9,)], [(1, 6, 5, 3, 4, 2), (7, 8), (9,)], [(1, 6, 5), (2, 4), (3,), (7, 8), (9,)], [(1, 6, 5, 2, 4), (3,), (7, 8), (9,)], [(1, 6, 5, 2, 4, 3), (7, 8), (9,)], [(1, 6, 5, 3, 2, 4), (7, 8), (9,)], [(1, 6, 5, 3), (2, 4), (7, 8), (9,)], [(1, 6, 4), (2, 3), (5,), (7, 8), (9,)], [(1, 6, 4, 2, 3), (5,), (7, 8), (9,)], [(1, 6, 4, 2), (3,), (5,), (7, 8), (9,)], [(1, 6, 4, 3), (2,), (5,), (7, 8), (9,)], [(1, 6, 4, 3, 2), (5,), (7, 8), 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8, 5), (6, 7), (9,)], [(1, 3), (2,), (4, 8, 6, 7, 5), (9,)], [(1, 3, 2), (4, 8, 6, 7, 5), (9,)], [(1,), (2, 3), (4, 8, 6, 7, 5), (9,)], [(1, 2), (3,), (4, 8, 6, 7, 5), (9,)], [(1,), (2,), (3,), (4, 8, 6, 7, 5), (9,)], [(1, 3), (2,), (4, 8), (5, 7), (6,), (9,)], [(1, 3, 2), (4, 8), (5, 7), (6,), (9,)], [(1,), (2, 3), (4, 8), (5, 7), (6,), (9,)], [(1, 2), (3,), (4, 8), (5, 7), (6,), (9,)], [(1,), (2,), (3,), (4, 8), (5, 7), (6,), (9,)], [(1, 3), (2,), (4, 8, 5, 7), (6,), (9,)], [(1, 3, 2), (4, 8, 5, 7), (6,), (9,)], [(1,), (2, 3), (4, 8, 5, 7), (6,), (9,)], [(1, 2), (3,), (4, 8, 5, 7), (6,), (9,)], [(1,), (2,), (3,), (4, 8, 5, 7), (6,), (9,)], [(1, 3), (2,), (4, 8, 5, 7, 6), (9,)], [(1, 3, 2), (4, 8, 5, 7, 6), (9,)], [(1,), (2, 3), (4, 8, 5, 7, 6), (9,)], [(1, 2), (3,), (4, 8, 5, 7, 6), (9,)], [(1,), (2,), (3,), (4, 8, 5, 7, 6), (9,)], [(1, 3), (2,), (4, 8, 6, 5, 7), (9,)], [(1, 3, 2), (4, 8, 6, 5, 7), (9,)], [(1,), (2, 3), (4, 8, 6, 5, 7), (9,)], [(1, 2), (3,), (4, 8, 6, 5, 7), (9,)], [(1,), (2,), (3,), (4, 8, 6, 5, 7), (9,)], [(1, 3), (2,), (4, 8, 6), (5, 7), (9,)], [(1, 3, 2), (4, 8, 6), (5, 7), (9,)], [(1,), (2, 3), (4, 8, 6), (5, 7), (9,)], [(1, 2), (3,), (4, 8, 6), (5, 7), (9,)], [(1,), (2,), (3,), (4, 8, 6), (5, 7), (9,)], [(1, 2), (3, 8, 7, 6), (4, 5), (9,)], [(1,), (2,), (3, 8, 7, 6), (4, 5), (9,)], [(1, 2), (3, 8, 7, 6, 4, 5), (9,)], [(1,), (2,), (3, 8, 7, 6, 4, 5), (9,)], [(1, 2), (3, 8, 7, 6, 4), (5,), (9,)], [(1,), (2,), (3, 8, 7, 6, 4), (5,), (9,)], [(1, 2), (3, 8, 7, 6, 5), (4,), (9,)], [(1,), (2,), (3, 8, 7, 6, 5), (4,), (9,)], [(1, 2), (3, 8, 7, 6, 5, 4), (9,)], [(1,), (2,), (3, 8, 7, 6, 5, 4), (9,)], [(1, 2), (3, 8, 7, 5), (4,), (6,), (9,)], [(1,), (2,), (3, 8, 7, 5), (4,), (6,), (9,)], [(1, 2), (3, 8, 7, 5, 4), (6,), (9,)], [(1,), (2,), (3, 8, 7, 5, 4), (6,), (9,)], [(1, 2), (3, 8, 7, 4), (5, 6), (9,)], [(1,), (2,), (3, 8, 7, 4), (5, 6), (9,)], [(1, 2), (3, 8, 7, 5, 6, 4), (9,)], [(1,), (2,), (3, 8, 7, 5, 6, 4), (9,)], [(1, 2), (3, 8, 7), (4, 6), (5,), (9,)], [(1,), (2,), (3, 8, 7), (4, 6), (5,), (9,)], [(1, 2), (3, 8, 7, 4, 6), (5,), (9,)], [(1,), (2,), (3, 8, 7, 4, 6), (5,), (9,)], [(1, 2), (3, 8, 7, 4, 6, 5), (9,)], [(1,), (2,), (3, 8, 7, 4, 6, 5), (9,)], [(1, 2), (3, 8, 7, 5, 4, 6), (9,)], [(1,), (2,), (3, 8, 7, 5, 4, 6), (9,)], [(1, 2), (3, 8, 7, 5), (4, 6), (9,)], [(1,), (2,), (3, 8, 7, 5), (4, 6), (9,)], [(1, 2), (3, 8, 6), (4, 5), (7,), (9,)], [(1,), (2,), (3, 8, 6), (4, 5), (7,), (9,)], [(1, 2), (3, 8, 6, 4, 5), (7,), (9,)], [(1,), (2,), (3, 8, 6, 4, 5), (7,), (9,)], [(1, 2), (3, 8, 6, 4), (5,), (7,), (9,)], [(1,), (2,), (3, 8, 6, 4), (5,), (7,), (9,)], [(1, 2), (3, 8, 6, 5), (4,), (7,), (9,)], [(1,), (2,), (3, 8, 6, 5), (4,), (7,), (9,)], [(1, 2), (3, 8, 6, 5, 4), (7,), (9,)], [(1,), (2,), (3, 8, 6, 5, 4), (7,), (9,)], [(1, 2), (3, 8, 5), (4,), (6, 7), (9,)], [(1,), (2,), (3, 8, 5), (4,), (6, 7), (9,)], [(1, 2), (3, 8, 5, 4), (6, 7), (9,)], [(1,), (2,), (3, 8, 5, 4), (6, 7), (9,)], [(1, 2), (3, 8, 6, 7, 5), (4,), (9,)], [(1,), (2,), (3, 8, 6, 7, 5), (4,), (9,)], [(1, 2), (3, 8, 6, 7, 5, 4), (9,)], [(1,), (2,), (3, 8, 6, 7, 5, 4), (9,)], [(1, 2), (3, 8, 4), (5, 7), (6,), (9,)], [(1,), (2,), (3, 8, 4), (5, 7), (6,), (9,)], [(1, 2), (3, 8, 5, 7, 4), (6,), (9,)], [(1,), (2,), (3, 8, 5, 7, 4), (6,), (9,)], [(1, 2), (3, 8, 5, 7, 6, 4), (9,)], [(1,), (2,), (3, 8, 5, 7, 6, 4), (9,)], [(1, 2), (3, 8, 6, 5, 7, 4), (9,)], [(1,), (2,), (3, 8, 6, 5, 7, 4), (9,)], [(1, 2), (3, 8, 6, 4), (5, 7), (9,)], [(1,), (2,), (3, 8, 6, 4), (5, 7), (9,)], [(1, 2), (3, 8, 6, 4, 7), (5,), (9,)], [(1,), (2,), (3, 8, 6, 4, 7), (5,), (9,)], [(1, 2), (3, 8, 6), (4, 7), (5,), (9,)], [(1,), (2,), (3, 8, 6), (4, 7), (5,), (9,)], [(1, 2), (3, 8, 6, 5), (4, 7), (9,)], [(1,), (2,), (3, 8, 6, 5), (4, 7), (9,)], [(1, 2), (3, 8, 6), (4, 7, 5), (9,)], [(1,), (2,), (3, 8, 6), (4, 7, 5), (9,)], [(1, 2), (3, 8, 6, 4, 7, 5), (9,)], [(1,), (2,), (3, 8, 6, 4, 7, 5), (9,)], [(1, 2), (3, 8, 5, 4, 7, 6), (9,)], [(1,), (2,), (3, 8, 5, 4, 7, 6), (9,)], [(1, 2), (3, 8, 5), (4, 7, 6), (9,)], [(1,), (2,), (3, 8, 5), (4, 7, 6), (9,)], [(1, 2), (3, 8, 4, 7, 5), (6,), (9,)], [(1,), (2,), (3, 8, 4, 7, 5), (6,), (9,)], [(1, 2), (3, 8, 5), (4, 7), (6,), (9,)], [(1,), (2,), (3, 8, 5), (4, 7), (6,), (9,)], [(1, 2), (3, 8), (4, 7), (5, 6), (9,)], [(1,), (2,), (3, 8), (4, 7), (5, 6), (9,)], [(1, 2), (3, 8, 4, 7), (5, 6), (9,)], [(1,), (2,), (3, 8, 4, 7), (5, 6), (9,)], [(1, 2), (3, 8, 4, 7, 5, 6), (9,)], [(1,), (2,), (3, 8, 4, 7, 5, 6), (9,)], [(1, 2), (3, 8, 5, 6, 4, 7), (9,)], [(1,), (2,), (3, 8, 5, 6, 4, 7), (9,)], [(1, 2), (3, 8, 5, 6), (4, 7), (9,)], [(1,), (2,), (3, 8, 5, 6), (4, 7), (9,)], [(1,), (2, 8, 7, 6, 5), (3, 4), (9,)], [(1,), (2, 8, 7, 6, 5, 3, 4), (9,)], [(1,), (2, 8, 7, 6, 5, 3), (4,), (9,)], [(1,), (2, 8, 7, 6, 5, 4), (3,), (9,)], [(1,), (2, 8, 7, 6, 5, 4, 3), (9,)], [(1,), (2, 8, 7, 6, 4), (3,), (5,), (9,)], [(1,), (2, 8, 7, 6, 4, 3), (5,), (9,)], [(1,), (2, 8, 7, 6, 3), (4, 5), (9,)], [(1,), (2, 8, 7, 6, 4, 5, 3), (9,)], [(1,), (2, 8, 7, 6), (3, 5), (4,), (9,)], [(1,), (2, 8, 7, 6, 3, 5), (4,), (9,)], [(1,), (2, 8, 7, 6, 3, 5, 4), (9,)], [(1,), (2, 8, 7, 6, 4, 3, 5), (9,)], [(1,), (2, 8, 7, 6, 4), (3, 5), (9,)], [(1,), (2, 8, 7, 5), (3, 4), (6,), (9,)], [(1,), (2, 8, 7, 5, 3, 4), (6,), (9,)], [(1,), (2, 8, 7, 5, 3), (4,), (6,), (9,)], [(1,), (2, 8, 7, 5, 4), (3,), (6,), (9,)], [(1,), (2, 8, 7, 5, 4, 3), (6,), (9,)], [(1,), (2, 8, 7, 4), (3,), (5, 6), (9,)], [(1,), (2, 8, 7, 4, 3), (5, 6), (9,)], [(1,), (2, 8, 7, 5, 6, 4), (3,), (9,)], [(1,), (2, 8, 7, 5, 6, 4, 3), (9,)], [(1,), (2, 8, 7, 3), (4, 6), (5,), (9,)], [(1,), (2, 8, 7, 4, 6, 3), (5,), (9,)], [(1,), (2, 8, 7, 4, 6, 5, 3), (9,)], [(1,), (2, 8, 7, 5, 4, 6, 3), (9,)], [(1,), (2, 8, 7, 5, 3), (4, 6), (9,)], [(1,), (2, 8, 7, 5, 3, 6), (4,), (9,)], [(1,), (2, 8, 7, 5), (3, 6), (4,), (9,)], [(1,), (2, 8, 7, 5, 4), (3, 6), (9,)], [(1,), (2, 8, 7, 5), (3, 6, 4), (9,)], [(1,), (2, 8, 7, 5, 3, 6, 4), (9,)], [(1,), (2, 8, 7, 4, 3, 6, 5), (9,)], [(1,), (2, 8, 7, 4), (3, 6, 5), (9,)], [(1,), (2, 8, 7, 3, 6, 4), (5,), (9,)], [(1,), (2, 8, 7, 4), (3, 6), (5,), (9,)], [(1,), (2, 8, 7), (3, 6), (4, 5), (9,)], [(1,), (2, 8, 7, 3, 6), (4, 5), (9,)], [(1,), (2, 8, 7, 3, 6, 4, 5), (9,)], [(1,), (2, 8, 7, 4, 5, 3, 6), (9,)], [(1,), (2, 8, 7, 4, 5), (3, 6), (9,)], [(1,), (2, 8, 6, 5), (3, 4), (7,), (9,)], [(1,), (2, 8, 6, 5, 3, 4), (7,), (9,)], [(1,), (2, 8, 6, 5, 3), (4,), (7,), (9,)], [(1,), (2, 8, 6, 5, 4), (3,), (7,), (9,)], [(1,), (2, 8, 6, 5, 4, 3), (7,), (9,)], [(1,), (2, 8, 6, 4), (3,), (5,), (7,), (9,)], [(1,), (2, 8, 6, 4, 3), (5,), (7,), (9,)], [(1,), (2, 8, 6, 3), (4, 5), (7,), (9,)], [(1,), (2, 8, 6, 4, 5, 3), (7,), (9,)], [(1,), (2, 8, 6), (3, 5), (4,), (7,), (9,)], [(1,), (2, 8, 6, 3, 5), (4,), (7,), (9,)], [(1,), (2, 8, 6, 3, 5, 4), (7,), (9,)], [(1,), (2, 8, 6, 4, 3, 5), (7,), (9,)], [(1,), (2, 8, 6, 4), (3, 5), (7,), (9,)], [(1,), (2, 8, 5), (3, 4), (6, 7), (9,)], [(1,), (2, 8, 5, 3, 4), (6, 7), (9,)], [(1,), (2, 8, 5, 3), (4,), (6, 7), (9,)], [(1,), (2, 8, 5, 4), (3,), (6, 7), (9,)], [(1,), (2, 8, 5, 4, 3), (6, 7), (9,)], [(1,), (2, 8, 6, 7, 5), (3, 4), (9,)], [(1,), (2, 8, 6, 7, 5, 3, 4), (9,)], [(1,), (2, 8, 6, 7, 5, 3), (4,), (9,)], [(1,), (2, 8, 6, 7, 5, 4), (3,), (9,)], [(1,), (2, 8, 6, 7, 5, 4, 3), (9,)], [(1,), (2, 8, 4), (3,), (5, 7), (6,), (9,)], [(1,), (2, 8, 4, 3), (5, 7), (6,), (9,)], [(1,), (2, 8, 5, 7, 4), (3,), (6,), (9,)], [(1,), (2, 8, 5, 7, 4, 3), (6,), (9,)], [(1,), (2, 8, 5, 7, 6, 4), (3,), (9,)], [(1,), (2, 8, 5, 7, 6, 4, 3), (9,)], [(1,), (2, 8, 6, 5, 7, 4), (3,), (9,)], [(1,), (2, 8, 6, 5, 7, 4, 3), (9,)], [(1,), (2, 8, 6, 4), (3,), (5, 7), (9,)], [(1,), (2, 8, 6, 4, 3), (5, 7), (9,)], [(1,), (2, 8, 6, 4, 7, 3), (5,), (9,)], [(1,), (2, 8, 6, 3), (4, 7), (5,), (9,)], [(1,), (2, 8, 6, 5, 3), (4, 7), (9,)], [(1,), (2, 8, 6, 3), (4, 7, 5), (9,)], [(1,), (2, 8, 6, 4, 7, 5, 3), (9,)], [(1,), (2, 8, 5, 4, 7, 6, 3), (9,)], [(1,), (2, 8, 5, 3), (4, 7, 6), (9,)], [(1,), (2, 8, 4, 7, 5, 3), (6,), (9,)], [(1,), (2, 8, 5, 3), (4, 7), (6,), (9,)],[...]
New=[] for i in [0..len(cycles)-1]: for j in [0..n-2]: if cycles[i][0][j]==2: if cycles[i][0][j+1]==n-1: New.append(cycles[i][0]) print New len(New)
[(1, 9, 7, 5, 2, 8, 6, 4, 3), (1, 9, 7, 5, 3, 2, 8, 6, 4), (1, 9, 7, 5, 4, 2, 8, 6, 3), (1, 9, 7, 5, 2, 8, 6, 3, 4), (1, 9, 7, 4, 2, 8, 6, 5, 3), (1, 9, 7, 4, 5, 2, 8, 6, 3), (1, 9, 7, 4, 3, 5, 2, 8, 6), (1, 9, 7, 4, 2, 8, 6, 3, 5), (1, 9, 7, 3, 5, 2, 8, 6, 4), (1, 9, 7, 2, 8, 6, 3, 5, 4), (1, 9, 7, 6, 4, 2, 8, 5, 3), (1, 9, 7, 6, 3, 2, 8, 5, 4), (1, 9, 7, 6, 2, 8, 5, 3, 4), (1, 9, 7, 6, 3, 4, 2, 8, 5), (1, 9, 7, 5, 6, 3, 2, 8, 4), (1, 9, 7, 3, 2, 8, 5, 6, 4), (1, 9, 7, 4, 2, 8, 5, 6, 3), (1, 9, 7, 2, 8, 5, 4, 6, 3), (1, 9, 7, 4, 6, 2, 8, 5, 3), (1, 9, 7, 5, 2, 8, 4, 6, 3), (1, 9, 7, 4, 6, 5, 2, 8, 3), (1, 9, 7, 4, 3, 6, 2, 8, 5), (1, 9, 7, 3, 6, 4, 2, 8, 5), (1, 9, 7, 3, 6, 2, 8, 5, 4), (1, 9, 7, 5, 2, 8, 4, 3, 6), (1, 9, 7, 5, 3, 6, 2, 8, 4), (1, 9, 7, 4, 2, 8, 3, 6, 5), (1, 9, 7, 3, 6, 5, 2, 8, 4), (1, 9, 7, 2, 8, 4, 5, 3, 6), (1, 9, 7, 3, 6, 2, 8, 4, 5), (1, 9, 7, 4, 5, 2, 8, 3, 6), (1, 9, 7, 2, 8, 3, 6, 4, 5), (1, 9, 6, 4, 2, 8, 7, 5, 3), (1, 9, 6, 3, 2, 8, 7, 5, 4), (1, 9, 6, 2, 8, 7, 5, 3, 4), (1, 9, 6, 3, 4, 2, 8, 7, 5), (1, 9, 6, 5, 2, 8, 7, 4, 3), (1, 9, 6, 5, 3, 2, 8, 7, 4), (1, 9, 6, 4, 5, 2, 8, 7, 3), (1, 9, 6, 2, 8, 7, 4, 5, 3), (1, 9, 6, 2, 8, 7, 4, 3, 5), (1, 9, 6, 3, 5, 2, 8, 7, 4), (1, 9, 6, 4, 2, 8, 7, 3, 5), (1, 9, 6, 2, 8, 7, 3, 5, 4), (1, 9, 5, 2, 8, 6, 7, 4, 3), (1, 9, 5, 3, 2, 8, 6, 7, 4), (1, 9, 6, 7, 5, 2, 8, 4, 3), (1, 9, 6, 7, 5, 3, 2, 8, 4), (1, 9, 6, 7, 4, 2, 8, 5, 3), (1, 9, 6, 5, 7, 4, 2, 8, 3), (1, 9, 6, 5, 7, 3, 2, 8, 4), (1, 9, 6, 4, 2, 8, 5, 7, 3), (1, 9, 6, 3, 2, 8, 5, 7, 4), (1, 9, 5, 7, 3, 2, 8, 6, 4), (1, 9, 5, 7, 4, 2, 8, 6, 3), (1, 9, 4, 2, 8, 5, 7, 6, 3), (1, 9, 5, 7, 6, 3, 2, 8, 4), (1, 9, 6, 2, 8, 5, 4, 7, 3), (1, 9, 6, 2, 8, 4, 7, 5, 3), (1, 9, 6, 5, 2, 8, 4, 7, 3), (1, 9, 5, 4, 7, 2, 8, 6, 3), (1, 9, 5, 2, 8, 6, 4, 7, 3), (1, 9, 4, 7, 6, 2, 8, 5, 3), (1, 9, 5, 2, 8, 4, 7, 6, 3), (1, 9, 5, 6, 4, 7, 2, 8, 3), (1, 9, 5, 6, 2, 8, 4, 7, 3), (1, 9, 4, 7, 2, 8, 5, 6, 3), (1, 9, 4, 7, 5, 6, 2, 8, 3), (1, 9, 6, 2, 8, 5, 3, 7, 4), (1, 9, 6, 3, 7, 4, 2, 8, 5), (1, 9, 6, 3, 7, 2, 8, 5, 4), (1, 9, 6, 2, 8, 4, 3, 7, 5), (1, 9, 6, 3, 7, 5, 2, 8, 4), (1, 9, 6, 5, 2, 8, 3, 7, 4), (1, 9, 6, 2, 8, 4, 5, 3, 7), (1, 9, 6, 3, 7, 2, 8, 4, 5), (1, 9, 6, 2, 8, 3, 7, 4, 5), (1, 9, 5, 2, 8, 6, 3, 7, 4), (1, 9, 4, 3, 7, 6, 2, 8, 5), (1, 9, 5, 2, 8, 4, 3, 7, 6), (1, 9, 5, 3, 7, 6, 2, 8, 4), (1, 9, 5, 6, 2, 8, 3, 7, 4), (1, 9, 5, 6, 3, 7, 2, 8, 4), (1, 9, 3, 7, 5, 6, 2, 8, 4), (1, 9, 5, 3, 7, 2, 8, 4, 6), (1, 9, 5, 2, 8, 3, 7, 4, 6), (1, 9, 5, 4, 6, 3, 7, 2, 8), (1, 9, 5, 4, 6, 2, 8, 3, 7), (1, 9, 4, 6, 2, 8, 5, 3, 7), (1, 9, 4, 6, 3, 7, 2, 8, 5), (1, 9, 3, 7, 5, 2, 8, 4, 6), (1, 9, 4, 6, 2, 8, 3, 7, 5), (1, 9, 2, 8, 3, 7, 4, 6, 5), (1, 9, 3, 7, 2, 8, 4, 6, 5)] 94
Permutation([6,5,4,2,1,3]).has_pattern([1,2,3]) Permutation([6,5,4,2,1,3]).has_pattern([1,3,2]) Permutation([6,5,4,2,1,3]).has_pattern([2,1,3]) Permutation([6,5,4,2,1,3]).has_pattern([2,3,1]) Permutation([6,5,4,2,1,3]).has_pattern([3,2,1]) Permutation([6,5,4,2,1,3]).has_pattern([3,1,2])
False False True False True True
P=Permutations(n, avoiding=[2,3,1]) P=P.list() print P len(P)
[[3, 2, 1, 4], [3, 1, 2, 4], [1, 3, 2, 4], [2, 1, 3, 4], [1, 2, 3, 4], [2, 1, 4, 3], [1, 2, 4, 3], [1, 4, 3, 2], [1, 4, 2, 3], [4, 3, 2, 1], [4, 3, 1, 2], [4, 1, 3, 2], [4, 2, 1, 3], [4, 1, 2, 3]] 14
def is_involution(p): return p == p.inverse()
n=6 L=[] P=Permutations(n, avoiding=[2,3,1]) for i in [0..len(P)-1]: if P[i][0]==n: L.append(P[i]) print L len(L)
[[6, 3, 2, 1, 4, 5], [6, 3, 1, 2, 4, 5], [6, 1, 3, 2, 4, 5], [6, 2, 1, 3, 4, 5], [6, 1, 2, 3, 4, 5], [6, 2, 1, 4, 3, 5], [6, 1, 2, 4, 3, 5], [6, 1, 4, 3, 2, 5], [6, 1, 4, 2, 3, 5], [6, 4, 3, 2, 1, 5], [6, 4, 3, 1, 2, 5], [6, 4, 1, 3, 2, 5], [6, 4, 2, 1, 3, 5], [6, 4, 1, 2, 3, 5], [6, 3, 2, 1, 5, 4], [6, 3, 1, 2, 5, 4], [6, 1, 3, 2, 5, 4], [6, 2, 1, 3, 5, 4], [6, 1, 2, 3, 5, 4], [6, 2, 1, 5, 4, 3], [6, 1, 2, 5, 4, 3], [6, 2, 1, 5, 3, 4], [6, 1, 2, 5, 3, 4], [6, 1, 5, 4, 3, 2], [6, 1, 5, 4, 2, 3], [6, 1, 5, 2, 4, 3], [6, 1, 5, 3, 2, 4], [6, 1, 5, 2, 3, 4], [6, 5, 3, 2, 1, 4], [6, 5, 3, 1, 2, 4], [6, 5, 1, 3, 2, 4], [6, 5, 2, 1, 3, 4], [6, 5, 1, 2, 3, 4], [6, 5, 2, 1, 4, 3], [6, 5, 1, 2, 4, 3], [6, 5, 1, 4, 3, 2], [6, 5, 1, 4, 2, 3], [6, 5, 4, 3, 2, 1], [6, 5, 4, 3, 1, 2], [6, 5, 4, 1, 3, 2], [6, 5, 4, 2, 1, 3], [6, 5, 4, 1, 2, 3]] 42
n=7 P=Permutations(n, avoiding=[2,3,1]) L=[] for i in [0..len(P)-1]: if P[i].has_pattern([3,2,1]): if P[i].has_pattern([3,1,2]): if P[i][0]==n: if P[i][1]==n-1: if P[i][n-1]!=1: if P[i][n-2]!=2: if P[i].has_pattern([1,2,3]): if P[i].has_pattern([1,3,2]): if P[i].has_pattern([2,1,3]): L.append(P[i]) # if P[i].has_pattern([2,1,3]): # if P[i].has_pattern([2,3,1]): # if P[i].has_pattern([3,1,2]): # if P[i].has_pattern([3,2,1]): # if P[i][0]==1: # if P[i][1]==n: # L.append(P[i]) print L len(L)
[[7, 6, 1, 3, 2, 4, 5], [7, 6, 2, 1, 4, 3, 5], [7, 6, 1, 2, 4, 3, 5], [7, 6, 1, 4, 2, 3, 5], [7, 6, 3, 1, 2, 5, 4], [7, 6, 1, 3, 2, 5, 4], [7, 6, 2, 1, 3, 5, 4], [7, 6, 2, 1, 5, 3, 4]] 8
n=7 P=Permutations(n, avoiding=[2,3,1]) L=[] d=[] D=[] for i in [0..len(P)-1]: if P[i].has_pattern([1,3,2]): if P[i].has_pattern([2,1,3]): if P[i][0]==n: if P[i][1]==n-1: if P[i][n-1]!=1: if P[i][n-2]!=2: if P[i][2]!=3: if P[i][3]!=4: if P[i][4]!=5: if P[i][5]!=6: if P[i][6]!=7: # if P[i][7]!=8: # if P[i][8]!=9: L.append(P[i]) for j in [0..len(L)-1]: d.append(L[j].inversions()) for k in [0..len(d)-1]: D.append(len(d[k])) print L len(L) print D len(D)
[[7, 6, 1, 3, 2, 4, 5], [7, 6, 2, 1, 4, 3, 5], [7, 6, 1, 2, 4, 3, 5], [7, 6, 1, 3, 2, 5, 4], [7, 6, 2, 1, 3, 5, 4], [7, 6, 5, 2, 1, 4, 3]] 6 [12, 13, 12, 13, 13, 17] 6
even=[] for i in [0..len(D)-1]: if D[i]%2==0: even.append(D[i]) len(even)
39
n=6 P=Permutations(n, avoiding=[2,3,1]) P.list() Q=[] for i in [0..len(P)-1]: Q.append(P[i].to_cycles()) #turn all the avoiding oneliners into their cycle notation print Q notcycles=[] cycles=[] for i in [0..len(Q)-1]: if len(Q[i])==1: cycles.append(Q[i]) else: notcycles.append(Q[i]) print cycles #print notcycles print len(cycles) B=[] #print len(notcycles) for i in [0..32]: B.append(cycles[53+i]) print B len(B)
[[3, 2, 1, 4, 5, 6], [3, 1, 2, 4, 5, 6], [1, 3, 2, 4, 5, 6], [2, 1, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6], [2, 1, 4, 3, 5, 6], [1, 2, 4, 3, 5, 6], [1, 4, 3, 2, 5, 6], [1, 4, 2, 3, 5, 6], [4, 3, 2, 1, 5, 6], [4, 3, 1, 2, 5, 6], [4, 1, 3, 2, 5, 6], [4, 2, 1, 3, 5, 6], [4, 1, 2, 3, 5, 6], [3, 2, 1, 5, 4, 6], [3, 1, 2, 5, 4, 6], [1, 3, 2, 5, 4, 6], [2, 1, 3, 5, 4, 6], [1, 2, 3, 5, 4, 6], [2, 1, 5, 4, 3, 6], [1, 2, 5, 4, 3, 6], [2, 1, 5, 3, 4, 6], [1, 2, 5, 3, 4, 6], [1, 5, 4, 3, 2, 6], [1, 5, 4, 2, 3, 6], [1, 5, 2, 4, 3, 6], [1, 5, 3, 2, 4, 6], [1, 5, 2, 3, 4, 6], [5, 3, 2, 1, 4, 6], [5, 3, 1, 2, 4, 6], [5, 1, 3, 2, 4, 6], [5, 2, 1, 3, 4, 6], [5, 1, 2, 3, 4, 6], [5, 2, 1, 4, 3, 6], [5, 1, 2, 4, 3, 6], [5, 1, 4, 3, 2, 6], [5, 1, 4, 2, 3, 6], [5, 4, 3, 2, 1, 6], [5, 4, 3, 1, 2, 6], [5, 4, 1, 3, 2, 6], [5, 4, 2, 1, 3, 6], [5, 4, 1, 2, 3, 6], [3, 2, 1, 4, 6, 5], [3, 1, 2, 4, 6, 5], [1, 3, 2, 4, 6, 5], [2, 1, 3, 4, 6, 5], [1, 2, 3, 4, 6, 5], [2, 1, 4, 3, 6, 5], [1, 2, 4, 3, 6, 5], [1, 4, 3, 2, 6, 5], [1, 4, 2, 3, 6, 5], [4, 3, 2, 1, 6, 5], [4, 3, 1, 2, 6, 5], [4, 1, 3, 2, 6, 5], [4, 2, 1, 3, 6, 5], [4, 1, 2, 3, 6, 5], [3, 2, 1, 6, 5, 4], [3, 1, 2, 6, 5, 4], [1, 3, 2, 6, 5, 4], [2, 1, 3, 6, 5, 4], [1, 2, 3, 6, 5, 4], [3, 2, 1, 6, 4, 5], [3, 1, 2, 6, 4, 5], [1, 3, 2, 6, 4, 5], [2, 1, 3, 6, 4, 5], [1, 2, 3, 6, 4, 5], [2, 1, 6, 5, 4, 3], [1, 2, 6, 5, 4, 3], [2, 1, 6, 5, 3, 4], [1, 2, 6, 5, 3, 4], [2, 1, 6, 3, 5, 4], [1, 2, 6, 3, 5, 4], [2, 1, 6, 4, 3, 5], [1, 2, 6, 4, 3, 5], [2, 1, 6, 3, 4, 5], [1, 2, 6, 3, 4, 5], [1, 6, 4, 3, 2, 5], [1, 6, 4, 2, 3, 5], [1, 6, 2, 4, 3, 5], [1, 6, 3, 2, 4, 5], [1, 6, 2, 3, 4, 5], [1, 6, 3, 2, 5, 4], [1, 6, 2, 3, 5, 4], [1, 6, 2, 5, 4, 3], [1, 6, 2, 5, 3, 4], [1, 6, 5, 4, 3, 2], [1, 6, 5, 4, 2, 3], [1, 6, 5, 2, 4, 3], [1, 6, 5, 3, 2, 4], [1, 6, 5, 2, 3, 4], [6, 3, 2, 1, 4, 5], [6, 3, 1, 2, 4, 5], [6, 1, 3, 2, 4, 5], [6, 2, 1, 3, 4, 5], [6, 1, 2, 3, 4, 5], [6, 2, 1, 4, 3, 5], [6, 1, 2, 4, 3, 5], [6, 1, 4, 3, 2, 5], [6, 1, 4, 2, 3, 5], [6, 4, 3, 2, 1, 5], [6, 4, 3, 1, 2, 5], [6, 4, 1, 3, 2, 5], [6, 4, 2, 1, 3, 5], [6, 4, 1, 2, 3, 5], [6, 3, 2, 1, 5, 4], [6, 3, 1, 2, 5, 4], [6, 1, 3, 2, 5, 4], [6, 2, 1, 3, 5, 4], [6, 1, 2, 3, 5, 4], [6, 2, 1, 5, 4, 3], [6, 1, 2, 5, 4, 3], [6, 2, 1, 5, 3, 4], [6, 1, 2, 5, 3, 4], [6, 1, 5, 4, 3, 2], [6, 1, 5, 4, 2, 3], [6, 1, 5, 2, 4, 3], [6, 1, 5, 3, 2, 4], [6, 1, 5, 2, 3, 4], [6, 5, 3, 2, 1, 4], [6, 5, 3, 1, 2, 4], [6, 5, 1, 3, 2, 4], [6, 5, 2, 1, 3, 4], [6, 5, 1, 2, 3, 4], [6, 5, 2, 1, 4, 3], [6, 5, 1, 2, 4, 3], [6, 5, 1, 4, 3, 2], [6, 5, 1, 4, 2, 3], [6, 5, 4, 3, 2, 1], [6, 5, 4, 3, 1, 2], [6, 5, 4, 1, 3, 2], [6, 5, 4, 2, 1, 3], [6, 5, 4, 1, 2, 3]] [[(1, 3), (2,), (4,), (5,), (6,)], [(1, 3, 2), (4,), (5,), (6,)], [(1,), (2, 3), (4,), (5,), (6,)], [(1, 2), (3,), (4,), (5,), (6,)], [(1,), (2,), (3,), (4,), (5,), (6,)], [(1, 2), (3, 4), (5,), (6,)], [(1,), (2,), (3, 4), (5,), (6,)], [(1,), (2, 4), (3,), (5,), (6,)], [(1,), (2, 4, 3), (5,), (6,)], [(1, 4), (2, 3), (5,), (6,)], [(1, 4, 2, 3), (5,), (6,)], [(1, 4, 2), (3,), (5,), (6,)], [(1, 4, 3), (2,), (5,), (6,)], [(1, 4, 3, 2), (5,), (6,)], [(1, 3), (2,), (4, 5), (6,)], [(1, 3, 2), (4, 5), (6,)], [(1,), (2, 3), (4, 5), (6,)], [(1, 2), (3,), (4, 5), (6,)], [(1,), (2,), (3,), (4, 5), (6,)], [(1, 2), (3, 5), (4,), (6,)], [(1,), (2,), (3, 5), (4,), (6,)], [(1, 2), (3, 5, 4), (6,)], [(1,), (2,), (3, 5, 4), (6,)], [(1,), (2, 5), (3, 4), (6,)], [(1,), (2, 5, 3, 4), (6,)], [(1,), (2, 5, 3), (4,), (6,)], [(1,), (2, 5, 4), (3,), (6,)], [(1,), (2, 5, 4, 3), (6,)], [(1, 5, 4), (2, 3), (6,)], [(1, 5, 4, 2, 3), (6,)], [(1, 5, 4, 2), (3,), (6,)], [(1, 5, 4, 3), (2,), (6,)], [(1, 5, 4, 3, 2), (6,)], [(1, 5, 3), (2,), (4,), (6,)], [(1, 5, 3, 2), (4,), (6,)], [(1, 5, 2), (3, 4), (6,)], [(1, 5, 3, 4, 2), (6,)], [(1, 5), (2, 4), (3,), (6,)], [(1, 5, 2, 4), (3,), (6,)], [(1, 5, 2, 4, 3), (6,)], [(1, 5, 3, 2, 4), (6,)], [(1, 5, 3), (2, 4), (6,)], [(1, 3), (2,), (4,), (5, 6)], [(1, 3, 2), (4,), (5, 6)], [(1,), (2, 3), (4,), (5, 6)], [(1, 2), (3,), (4,), (5, 6)], [(1,), (2,), (3,), (4,), (5, 6)], [(1, 2), (3, 4), (5, 6)], [(1,), (2,), (3, 4), (5, 6)], [(1,), (2, 4), (3,), (5, 6)], [(1,), (2, 4, 3), (5, 6)], [(1, 4), (2, 3), (5, 6)], [(1, 4, 2, 3), (5, 6)], [(1, 4, 2), (3,), (5, 6)], [(1, 4, 3), (2,), (5, 6)], [(1, 4, 3, 2), (5, 6)], [(1, 3), (2,), (4, 6), (5,)], [(1, 3, 2), (4, 6), (5,)], [(1,), (2, 3), (4, 6), (5,)], [(1, 2), (3,), (4, 6), (5,)], [(1,), (2,), (3,), (4, 6), (5,)], [(1, 3), (2,), (4, 6, 5)], [(1, 3, 2), (4, 6, 5)], [(1,), (2, 3), (4, 6, 5)], [(1, 2), (3,), (4, 6, 5)], [(1,), (2,), (3,), (4, 6, 5)], [(1, 2), (3, 6), (4, 5)], [(1,), (2,), (3, 6), (4, 5)], [(1, 2), (3, 6, 4, 5)], [(1,), (2,), (3, 6, 4, 5)], [(1, 2), (3, 6, 4), (5,)], [(1,), (2,), (3, 6, 4), (5,)], [(1, 2), (3, 6, 5), (4,)], [(1,), (2,), (3, 6, 5), (4,)], [(1, 2), (3, 6, 5, 4)], [(1,), (2,), (3, 6, 5, 4)], [(1,), (2, 6, 5), (3, 4)], [(1,), (2, 6, 5, 3, 4)], [(1,), (2, 6, 5, 3), (4,)], [(1,), (2, 6, 5, 4), (3,)], [(1,), (2, 6, 5, 4, 3)], [(1,), (2, 6, 4), (3,), (5,)], [(1,), (2, 6, 4, 3), (5,)], [(1,), (2, 6, 3), (4, 5)], [(1,), (2, 6, 4, 5, 3)], [(1,), (2, 6), (3, 5), (4,)], [(1,), (2, 6, 3, 5), (4,)], [(1,), (2, 6, 3, 5, 4)], [(1,), (2, 6, 4, 3, 5)], [(1,), (2, 6, 4), (3, 5)], [(1, 6, 5, 4), (2, 3)], [(1, 6, 5, 4, 2, 3)], [(1, 6, 5, 4, 2), (3,)], [(1, 6, 5, 4, 3), (2,)], [(1, 6, 5, 4, 3, 2)], [(1, 6, 5, 3), (2,), (4,)], [(1, 6, 5, 3, 2), (4,)], [(1, 6, 5, 2), (3, 4)], [(1, 6, 5, 3, 4, 2)], [(1, 6, 5), (2, 4), (3,)], [(1, 6, 5, 2, 4), (3,)], [(1, 6, 5, 2, 4, 3)], [(1, 6, 5, 3, 2, 4)], [(1, 6, 5, 3), (2, 4)], [(1, 6, 4), (2, 3), (5,)], [(1, 6, 4, 2, 3), (5,)], [(1, 6, 4, 2), (3,), (5,)], [(1, 6, 4, 3), (2,), (5,)], [(1, 6, 4, 3, 2), (5,)], [(1, 6, 3), (2,), (4, 5)], [(1, 6, 3, 2), (4, 5)], [(1, 6, 4, 5, 3), (2,)], [(1, 6, 4, 5, 3, 2)], [(1, 6, 2), (3, 5), (4,)], [(1, 6, 3, 5, 2), (4,)], [(1, 6, 3, 5, 4, 2)], [(1, 6, 4, 3, 5, 2)], [(1, 6, 4, 2), (3, 5)], [(1, 6, 4, 2, 5), (3,)], [(1, 6, 4), (2, 5), (3,)], [(1, 6, 4, 3), (2, 5)], [(1, 6, 4), (2, 5, 3)], [(1, 6, 4, 2, 5, 3)], [(1, 6, 3, 2, 5, 4)], [(1, 6, 3), (2, 5, 4)], [(1, 6, 2, 5, 3), (4,)], [(1, 6, 3), (2, 5), (4,)], [(1, 6), (2, 5), (3, 4)], [(1, 6, 2, 5), (3, 4)], [(1, 6, 2, 5, 3, 4)], [(1, 6, 3, 4, 2, 5)], [(1, 6, 3, 4), (2, 5)]] [[(1, 6, 5, 4, 2, 3)], [(1, 6, 5, 4, 3, 2)], [(1, 6, 5, 3, 4, 2)], [(1, 6, 5, 2, 4, 3)], [(1, 6, 5, 3, 2, 4)], [(1, 6, 4, 5, 3, 2)], [(1, 6, 3, 5, 4, 2)], [(1, 6, 4, 3, 5, 2)], [(1, 6, 4, 2, 5, 3)], [(1, 6, 3, 2, 5, 4)], [(1, 6, 2, 5, 3, 4)], [(1, 6, 3, 4, 2, 5)]] 12
Error in lines 18-19 Traceback (most recent call last): File "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 976, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 2, in <module> IndexError: list index out of range
D=[] d=[] for j in [0..len(cycles)-1]: d.append(Permutation([cycles[j][0]]).inversions()) for k in [0..len(d)-1]: D.append(len(d[k])) print D len(D)
[7, 5, 7, 9, 9, 7, 9, 9, 9, 11, 13, 13] 12
N=[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]] for i in [0..len(B)-1]: for j in [0..n-1]: N[i].append(B[i][0][j]) print N d=[] D=[] L=[] for j in [0..len(N)-1]: d.append(Permutation(N[j]).inversions()) for k in [0..len(d)-1]: D.append(len(d[k])) print D len(D)
[[1, 7, 5, 2, 6, 4, 3], [1, 7, 5, 3, 2, 6, 4], [1, 7, 5, 4, 2, 6, 3], [1, 7, 5, 2, 6, 3, 4], [1, 7, 4, 2, 6, 5, 3], [1, 7, 4, 5, 2, 6, 3], [1, 7, 4, 3, 5, 2, 6], [1, 7, 4, 2, 6, 3, 5], [1, 7, 3, 5, 2, 6, 4], [1, 7, 2, 6, 3, 5, 4], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], []] [11, 10, 11, 10, 10, 10, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 33
n=7 P=Permutations(n, avoiding=[2,3,1]) Q=[] D=[] d=[] for j in [0..len(P)-1]: if P[j][0]==n: Q.append(P[j].to_cycles()) d.append(P[j].inversions()) for k in [0..len(d)-1]: D.append(len(d[k])) print Q print D len(Q) len(D)
[[(1, 7, 6, 5, 4), (2, 3)], [(1, 7, 6, 5, 4, 2, 3)], [(1, 7, 6, 5, 4, 2), (3,)], [(1, 7, 6, 5, 4, 3), (2,)], [(1, 7, 6, 5, 4, 3, 2)], [(1, 7, 6, 5, 3), (2,), (4,)], [(1, 7, 6, 5, 3, 2), (4,)], [(1, 7, 6, 5, 2), (3, 4)], [(1, 7, 6, 5, 3, 4, 2)], [(1, 7, 6, 5), (2, 4), (3,)], [(1, 7, 6, 5, 2, 4), (3,)], [(1, 7, 6, 5, 2, 4, 3)], [(1, 7, 6, 5, 3, 2, 4)], [(1, 7, 6, 5, 3), (2, 4)], [(1, 7, 6, 4), (2, 3), (5,)], [(1, 7, 6, 4, 2, 3), (5,)], [(1, 7, 6, 4, 2), (3,), (5,)], [(1, 7, 6, 4, 3), (2,), (5,)], [(1, 7, 6, 4, 3, 2), (5,)], [(1, 7, 6, 3), (2,), (4, 5)], [(1, 7, 6, 3, 2), (4, 5)], [(1, 7, 6, 4, 5, 3), (2,)], [(1, 7, 6, 4, 5, 3, 2)], [(1, 7, 6, 2), (3, 5), (4,)], [(1, 7, 6, 3, 5, 2), (4,)], [(1, 7, 6, 3, 5, 4, 2)], [(1, 7, 6, 4, 3, 5, 2)], [(1, 7, 6, 4, 2), (3, 5)], [(1, 7, 6, 4, 2, 5), (3,)], [(1, 7, 6, 4), (2, 5), (3,)], [(1, 7, 6, 4, 3), (2, 5)], [(1, 7, 6, 4), (2, 5, 3)], [(1, 7, 6, 4, 2, 5, 3)], [(1, 7, 6, 3, 2, 5, 4)], [(1, 7, 6, 3), (2, 5, 4)], [(1, 7, 6, 2, 5, 3), (4,)], [(1, 7, 6, 3), (2, 5), (4,)], [(1, 7, 6), (2, 5), (3, 4)], [(1, 7, 6, 2, 5), (3, 4)], [(1, 7, 6, 2, 5, 3, 4)], [(1, 7, 6, 3, 4, 2, 5)], [(1, 7, 6, 3, 4), (2, 5)], [(1, 7, 5, 4), (2, 3), (6,)], [(1, 7, 5, 4, 2, 3), (6,)], [(1, 7, 5, 4, 2), (3,), (6,)], [(1, 7, 5, 4, 3), (2,), (6,)], [(1, 7, 5, 4, 3, 2), (6,)], [(1, 7, 5, 3), (2,), (4,), (6,)], [(1, 7, 5, 3, 2), (4,), (6,)], [(1, 7, 5, 2), (3, 4), (6,)], [(1, 7, 5, 3, 4, 2), (6,)], [(1, 7, 5), (2, 4), (3,), (6,)], [(1, 7, 5, 2, 4), (3,), (6,)], [(1, 7, 5, 2, 4, 3), (6,)], [(1, 7, 5, 3, 2, 4), (6,)], [(1, 7, 5, 3), (2, 4), (6,)], [(1, 7, 4), (2, 3), (5, 6)], [(1, 7, 4, 2, 3), (5, 6)], [(1, 7, 4, 2), (3,), (5, 6)], [(1, 7, 4, 3), (2,), (5, 6)], [(1, 7, 4, 3, 2), (5, 6)], [(1, 7, 5, 6, 4), (2, 3)], [(1, 7, 5, 6, 4, 2, 3)], [(1, 7, 5, 6, 4, 2), (3,)], [(1, 7, 5, 6, 4, 3), (2,)], [(1, 7, 5, 6, 4, 3, 2)], [(1, 7, 3), (2,), (4, 6), (5,)], [(1, 7, 3, 2), (4, 6), (5,)], [(1, 7, 4, 6, 3), (2,), (5,)], [(1, 7, 4, 6, 3, 2), (5,)], [(1, 7, 4, 6, 5, 3), (2,)], [(1, 7, 4, 6, 5, 3, 2)], [(1, 7, 5, 4, 6, 3), (2,)], [(1, 7, 5, 4, 6, 3, 2)], [(1, 7, 5, 3), (2,), (4, 6)], [(1, 7, 5, 3, 2), (4, 6)], [(1, 7, 5, 3, 6, 2), (4,)], [(1, 7, 5, 2), (3, 6), (4,)], [(1, 7, 5, 4, 2), (3, 6)], [(1, 7, 5, 2), (3, 6, 4)], [(1, 7, 5, 3, 6, 4, 2)], [(1, 7, 4, 3, 6, 5, 2)], [(1, 7, 4, 2), (3, 6, 5)], [(1, 7, 3, 6, 4, 2), (5,)], [(1, 7, 4, 2), (3, 6), (5,)], [(1, 7, 2), (3, 6), (4, 5)], [(1, 7, 3, 6, 2), (4, 5)], [(1, 7, 3, 6, 4, 5, 2)], [(1, 7, 4, 5, 3, 6, 2)], [(1, 7, 4, 5, 2), (3, 6)], [(1, 7, 5), (2, 6, 4), (3,)], [(1, 7, 5, 2, 6, 4), (3,)], [(1, 7, 5, 2, 6, 4, 3)], [(1, 7, 5, 3, 2, 6, 4)], [(1, 7, 5, 3), (2, 6, 4)], [(1, 7, 5, 4), (2, 6, 3)], [(1, 7, 5, 4, 2, 6, 3)], [(1, 7, 5, 3), (2, 6), (4,)], [(1, 7, 5, 2, 6, 3), (4,)], [(1, 7, 5, 2, 6), (3, 4)], [(1, 7, 5), (2, 6), (3, 4)], [(1, 7, 5, 3, 4), (2, 6)], [(1, 7, 5), (2, 6, 3, 4)], [(1, 7, 5, 2, 6, 3, 4)], [(1, 7, 4, 2, 6, 5), (3,)], [(1, 7, 4), (2, 6, 5), (3,)], [(1, 7, 4, 3), (2, 6, 5)], [(1, 7, 4), (2, 6, 5, 3)], [(1, 7, 4, 2, 6, 5, 3)], [(1, 7, 3, 2, 6, 4), (5,)], [(1, 7, 3), (2, 6, 4), (5,)], [(1, 7, 4), (2, 6, 3), (5,)], [(1, 7, 4, 2, 6, 3), (5,)], [(1, 7, 2, 6, 3), (4, 5)], [(1, 7, 3), (2, 6), (4, 5)], [(1, 7, 3), (2, 6, 4, 5)], [(1, 7, 4, 5, 3), (2, 6)], [(1, 7, 4, 5, 2, 6, 3)], [(1, 7, 4, 3, 5, 2, 6)], [(1, 7, 4, 3, 5), (2, 6)], [(1, 7, 4), (2, 6), (3, 5)], [(1, 7, 4, 2, 6, 3, 5)], [(1, 7, 4), (2, 6, 3, 5)], [(1, 7, 3, 5), (2, 6, 4)], [(1, 7, 3, 5, 2, 6, 4)], [(1, 7, 2, 6, 3, 5, 4)], [(1, 7, 3, 5, 4), (2, 6)], [(1, 7), (2, 6), (3, 5), (4,)], [(1, 7, 2, 6), (3, 5), (4,)], [(1, 7, 2, 6, 3, 5), (4,)], [(1, 7, 3, 5, 2, 6), (4,)], [(1, 7, 3, 5), (2, 6), (4,)]] [9, 8, 7, 7, 6, 8, 7, 9, 8, 12, 11, 10, 10, 9, 10, 9, 8, 8, 7, 10, 9, 9, 8, 12, 11, 10, 10, 9, 13, 12, 11, 11, 10, 12, 11, 13, 12, 16, 15, 14, 14, 13, 10, 9, 8, 8, 7, 9, 8, 10, 9, 13, 12, 11, 11, 10, 12, 11, 10, 10, 9, 11, 10, 9, 9, 8, 13, 12, 12, 11, 11, 10, 11, 10, 10, 9, 13, 12, 11, 11, 10, 12, 11, 13, 12, 16, 15, 14, 14, 13, 14, 13, 12, 12, 11, 13, 12, 14, 13, 17, 16, 15, 15, 14, 15, 14, 13, 13, 12, 15, 14, 14, 13, 17, 16, 15, 15, 14, 18, 17, 16, 16, 15, 17, 16, 18, 17, 21, 20, 19, 19, 18] 132 132
O=[] E=[] p=[] for i in [0..len(D)-1]: if D[i]%2==0: E.append(d[i]) p.append(Q[i]) else: O.append(d[i]) len(E) len(O) print p
66 66 [[(1, 7, 6, 5, 4, 2, 3)], [(1, 7, 6, 5, 4, 3, 2)], [(1, 7, 6, 5, 3), (2,), (4,)], [(1, 7, 6, 5, 3, 4, 2)], [(1, 7, 6, 5), (2, 4), (3,)], [(1, 7, 6, 5, 2, 4, 3)], [(1, 7, 6, 5, 3, 2, 4)], [(1, 7, 6, 4), (2, 3), (5,)], [(1, 7, 6, 4, 2), (3,), (5,)], [(1, 7, 6, 4, 3), (2,), (5,)], [(1, 7, 6, 3), (2,), (4, 5)], [(1, 7, 6, 4, 5, 3, 2)], [(1, 7, 6, 2), (3, 5), (4,)], [(1, 7, 6, 3, 5, 4, 2)], [(1, 7, 6, 4, 3, 5, 2)], [(1, 7, 6, 4), (2, 5), (3,)], [(1, 7, 6, 4, 2, 5, 3)], [(1, 7, 6, 3, 2, 5, 4)], [(1, 7, 6, 3), (2, 5), (4,)], [(1, 7, 6), (2, 5), (3, 4)], [(1, 7, 6, 2, 5, 3, 4)], [(1, 7, 6, 3, 4, 2, 5)], [(1, 7, 5, 4), (2, 3), (6,)], [(1, 7, 5, 4, 2), (3,), (6,)], [(1, 7, 5, 4, 3), (2,), (6,)], [(1, 7, 5, 3, 2), (4,), (6,)], [(1, 7, 5, 2), (3, 4), (6,)], [(1, 7, 5, 2, 4), (3,), (6,)], [(1, 7, 5, 3), (2, 4), (6,)], [(1, 7, 4), (2, 3), (5, 6)], [(1, 7, 4, 2), (3,), (5, 6)], [(1, 7, 4, 3), (2,), (5, 6)], [(1, 7, 5, 6, 4, 2, 3)], [(1, 7, 5, 6, 4, 3, 2)], [(1, 7, 3, 2), (4, 6), (5,)], [(1, 7, 4, 6, 3), (2,), (5,)], [(1, 7, 4, 6, 5, 3, 2)], [(1, 7, 5, 4, 6, 3, 2)], [(1, 7, 5, 3), (2,), (4, 6)], [(1, 7, 5, 2), (3, 6), (4,)], [(1, 7, 5, 3, 6, 4, 2)], [(1, 7, 4, 3, 6, 5, 2)], [(1, 7, 4, 2), (3, 6), (5,)], [(1, 7, 2), (3, 6), (4, 5)], [(1, 7, 3, 6, 4, 5, 2)], [(1, 7, 4, 5, 3, 6, 2)], [(1, 7, 5), (2, 6, 4), (3,)], [(1, 7, 5, 2, 6, 4, 3)], [(1, 7, 5, 3, 2, 6, 4)], [(1, 7, 5, 4, 2, 6, 3)], [(1, 7, 5, 3), (2, 6), (4,)], [(1, 7, 5), (2, 6), (3, 4)], [(1, 7, 5, 2, 6, 3, 4)], [(1, 7, 4), (2, 6, 5), (3,)], [(1, 7, 4, 2, 6, 5, 3)], [(1, 7, 3), (2, 6, 4), (5,)], [(1, 7, 4), (2, 6, 3), (5,)], [(1, 7, 3), (2, 6), (4, 5)], [(1, 7, 4, 5, 2, 6, 3)], [(1, 7, 4, 3, 5, 2, 6)], [(1, 7, 4), (2, 6), (3, 5)], [(1, 7, 4, 2, 6, 3, 5)], [(1, 7, 3, 5, 2, 6, 4)], [(1, 7, 2, 6, 3, 5, 4)], [(1, 7, 2, 6), (3, 5), (4,)], [(1, 7, 3, 5), (2, 6), (4,)]]
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