Root system: Root system of type ['A', 2]
Number of antichains of root poset: 5
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['A', 2]
Number of antichains of root poset: 5
Number fixed by Rvac: 1
Number fixed by Row^{-1}*Rvac: 3
Root system: Root system of type ['A', 3]
Number of antichains of root poset: 14
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['A', 3]
Number of antichains of root poset: 14
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 6
Root system: Root system of type ['A', 4]
Number of antichains of root poset: 42
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['A', 4]
Number of antichains of root poset: 42
Number fixed by Rvac: 2
Number fixed by Row^{-1}*Rvac: 10
Root system: Root system of type ['A', 5]
Number of antichains of root poset: 132
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['A', 5]
Number of antichains of root poset: 132
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 20
Root system: Root system of type ['A', 6]
Number of antichains of root poset: 429
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['A', 6]
Number of antichains of root poset: 429
Number fixed by Rvac: 5
Number fixed by Row^{-1}*Rvac: 35
Root system: Root system of type ['A', 7]
Number of antichains of root poset: 1430
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['A', 7]
Number of antichains of root poset: 1430
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 70
Root system: Root system of type ['A', 8]
Number of antichains of root poset: 4862
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['A', 8]
Number of antichains of root poset: 4862
Number fixed by Rvac: 14
Number fixed by Row^{-1}*Rvac: 126
Root system: Root system of type ['B', 2]
Number of antichains of root poset: 6
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['B', 2]
Number of antichains of root poset: 6
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 4
Root system: Root system of type ['B', 3]
Number of antichains of root poset: 20
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['B', 3]
Number of antichains of root poset: 20
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 8
Root system: Root system of type ['B', 4]
Number of antichains of root poset: 70
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['B', 4]
Number of antichains of root poset: 70
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 16
Root system: Root system of type ['B', 5]
Number of antichains of root poset: 252
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['B', 5]
Number of antichains of root poset: 252
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 32
Root system: Root system of type ['B', 6]
Number of antichains of root poset: 924
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['B', 6]
Number of antichains of root poset: 924
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 64
Root system: Root system of type ['B', 7]
Number of antichains of root poset: 3432
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['B', 7]
Number of antichains of root poset: 3432
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 128
Root system: Root system of type ['B', 8]
Number of antichains of root poset: 12870
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['B', 8]
Number of antichains of root poset: 12870
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 256
Root system: Root system of type ['D', 3]
Number of antichains of root poset: 14
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['D', 3]
Number of antichains of root poset: 14
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 6
Root system: Root system of type ['D', 4]
Number of antichains of root poset: 50
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['D', 4]
Number of antichains of root poset: 50
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 16
Root system: Root system of type ['D', 5]
Number of antichains of root poset: 182
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['D', 5]
Number of antichains of root poset: 182
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 26
Root system: Root system of type ['D', 6]
Number of antichains of root poset: 672
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['D', 6]
Number of antichains of root poset: 672
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 64
Root system: Root system of type ['D', 7]
Number of antichains of root poset: 2508
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['D', 7]
Number of antichains of root poset: 2508
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 108
Root system: Root system of type ['D', 8]
Number of antichains of root poset: 9438
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['D', 8]
Number of antichains of root poset: 9438
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 256
Root system: Root system of type ['G', 2]
Number of antichains of root poset: 8
Number of antichains for which #A + #Rvac(A) != rank: 0
Root system: Root system of type ['G', 2]
Number of antichains of root poset: 8
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 4
Root system: Root system of type ['F', 4]
Number of antichains of root poset: 105
Number of antichains for which #A + #Rvac(A) != rank: 8
An example of a failure: (3, [alpha[1] + 2*alpha[2] + 2*alpha[3] + 2*alpha[4]], [alpha[2] + 2*alpha[3] + alpha[4], alpha[1] + alpha[2] + alpha[3]])
Root system: Root system of type ['F', 4]
Number of antichains of root poset: 105
Number fixed by Rvac: 1
Number fixed by Row^{-1}*Rvac: 17
Root system: Root system of type ['E', 6]
Number of antichains of root poset: 833
Number of antichains for which #A + #Rvac(A) != rank: 24
An example of a failure: (5, [alpha[1] + alpha[2] + alpha[3] + 2*alpha[4] + alpha[5] + alpha[6]], [alpha[1] + alpha[3] + alpha[4] + alpha[5], alpha[2] + alpha[4] + alpha[5], alpha[2] + alpha[3] + alpha[4], alpha[3] + alpha[4] + alpha[5] + alpha[6]])
Root system: Root system of type ['E', 6]
Number of antichains of root poset: 833
Number fixed by Rvac: 5
Number fixed by Row^{-1}*Rvac: 47
Root system: Root system of type ['E', 7]
Number of antichains of root poset: 4160
Number of antichains for which #A + #Rvac(A) != rank: 354
An example of a failure: (9, [alpha[2] + alpha[3] + 2*alpha[4] + 2*alpha[5] + alpha[6], alpha[2] + alpha[4] + alpha[5] + alpha[6] + alpha[7], alpha[1] + alpha[2] + 2*alpha[3] + 2*alpha[4] + alpha[5], alpha[1] + alpha[2] + alpha[3] + alpha[4] + alpha[5] + alpha[6], alpha[1] + alpha[3] + alpha[4] + alpha[5] + alpha[6] + alpha[7]], [alpha[2] + alpha[3] + 2*alpha[4] + alpha[5] + alpha[6], alpha[2] + alpha[3] + alpha[4] + alpha[5] + alpha[6] + alpha[7], alpha[1] + alpha[3] + alpha[4] + alpha[5] + alpha[6] + alpha[7], alpha[1] + alpha[2] + 2*alpha[3] + 2*alpha[4] + alpha[5]])
Root system: Root system of type ['E', 7]
Number of antichains of root poset: 4160
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 132
Root system: Root system of type ['E', 8]
Number of antichains of root poset: 25080
Number of antichains for which #A + #Rvac(A) != rank: 4582
An example of a failure: (10, [2*alpha[1] + 2*alpha[2] + 3*alpha[3] + 4*alpha[4] + 3*alpha[5] + 2*alpha[6] + alpha[7], alpha[1] + alpha[2] + alpha[3] + 2*alpha[4] + 2*alpha[5] + 2*alpha[6] + 2*alpha[7] + alpha[8], alpha[1] + alpha[2] + 2*alpha[3] + 3*alpha[4] + 3*alpha[5] + 2*alpha[6] + alpha[7] + alpha[8], alpha[1] + 2*alpha[2] + 2*alpha[3] + 3*alpha[4] + 2*alpha[5] + alpha[6] + alpha[7] + alpha[8]], [alpha[2] + alpha[4] + alpha[5] + alpha[6] + alpha[7] + alpha[8], alpha[1] + alpha[2] + alpha[3] + 2*alpha[4] + alpha[5] + alpha[6], alpha[1] + alpha[3] + alpha[4] + alpha[5] + alpha[6] + alpha[7] + alpha[8], alpha[2] + alpha[3] + 2*alpha[4] + 2*alpha[5] + alpha[6], alpha[2] + alpha[3] + 2*alpha[4] + alpha[5] + alpha[6] + alpha[7], alpha[1] + alpha[2] + alpha[3] + alpha[4] + alpha[5] + alpha[6] + alpha[7]])
Root system: Root system of type ['E', 8]
Number of antichains of root poset: 25080
Number fixed by Rvac: 14
Number fixed by Row^{-1}*Rvac: 278
Number of antichains of root poset: 32
Number of antichains for which #A + #Rvac(A) != rank: 0
Number of antichains of root poset: 32
Number fixed by Rvac: 0
Number fixed by Row^{-1}*Rvac: 8
Weyl group: Finite Coxeter group over Number Field in a with defining polynomial x^2 - 5 with a = 2.236067977499790? with Coxeter matrix:
[1 3 2]
[3 1 5]
[2 5 1]
Number of noncrossing partitions: 32
Number fixed by Refl: 8
Number fixed by Krew*Refl: 0