Kernel: SageMath (stable)
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The Rise contact involution on Tamari Intervals
Viviane Pons -- July, 24th 2018 -- ICERM
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The Tamari lattice
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Some statistics on Dyck Paths
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2
2
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[2, 2, 0, 1, 0, 2, 0, 2, 0, 1]
[2, 2, 0, 0, 2, 2, 2, 0, 0, 0]
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True
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False
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[2, 2, 0, 1, 0, 2, 0, 2, 0, 1]
[2, 2, 2, 2, 1, 1, 0, 0, 0, 0]
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True
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True
Statistics on Tamari intervals
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13
[([1, 0, 1, 0, 1, 0], [1, 1, 1, 0, 0, 0]),
([1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 0]),
([1, 0, 1, 0, 1, 0], [1, 1, 0, 1, 0, 0]),
([1, 0, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0]),
([1, 1, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0]),
([1, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]),
([1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0]),
([1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 0, 0]),
([1, 1, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0]),
([1, 1, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0]),
([1, 0, 1, 0, 1, 0], [1, 0, 1, 1, 0, 0]),
([1, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0]),
([1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0])]
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[1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]
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[1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]
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[3, 0, 2, 0, 0, 4, 0, 0, 1, 0]
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[4, 3, 2, 1, 0, 0, 0, 0, 0, 0]
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[3, 1, 0, 2, 3, 0, 1, 0, 0, 0]
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[3, 3, 2, 1, 1, 0, 0, 0, 0, 0]
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True
Tamari Interval-Posets
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([1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0],
[1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0])
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[3, 0, 2, 0, 0, 4, 0, 0, 1, 0]
[4, 2, 0, 0, 1, 0, 2, 1, 0, 0]
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[3, 0, 4, 0, 0, 1, 0, 0, 2, 0]
[3, 1, 0, 2, 3, 0, 1, 0, 0, 0]
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[3, 3, 2, 1, 1, 0, 0, 0, 0, 0]
[4, 3, 2, 1, 0, 0, 0, 0, 0, 0]
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True
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