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Statistic identifier: St001637

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Collection: Posets

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Description: The number of (upper) dissectors of a poset.

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References: [1]   Reading, N. Order dimension, strong Bruhat order and lattice properties for posets [[MathSciNet:1902662]]

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Code:
def statistic(P):
    return sum(1 for u in P if len(P.panyushev_complement([u]))==1)

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Statistic values:

([],2)                                    => 2
([(0,1)],2)                               => 1
([],3)                                    => 0
([(1,2)],3)                               => 2
([(0,1),(0,2)],3)                         => 2
([(0,2),(2,1)],3)                         => 2
([(0,2),(1,2)],3)                         => 2
([],4)                                    => 0
([(2,3)],4)                               => 0
([(1,2),(1,3)],4)                         => 1
([(0,1),(0,2),(0,3)],4)                   => 0
([(0,2),(0,3),(3,1)],4)                   => 2
([(0,1),(0,2),(1,3),(2,3)],4)             => 2
([(1,2),(2,3)],4)                         => 2
([(0,3),(3,1),(3,2)],4)                   => 3
([(1,3),(2,3)],4)                         => 1
([(0,3),(1,3),(3,2)],4)                   => 3
([(0,3),(1,3),(2,3)],4)                   => 0
([(0,3),(1,2)],4)                         => 2
([(0,3),(1,2),(1,3)],4)                   => 3
([(0,2),(0,3),(1,2),(1,3)],4)             => 4
([(0,3),(2,1),(3,2)],4)                   => 3
([(0,3),(1,2),(2,3)],4)                   => 2
([],5)                                    => 0
([(3,4)],5)                               => 0
([(2,3),(2,4)],5)                         => 0
([(1,2),(1,3),(1,4)],5)                   => 1
([(0,1),(0,2),(0,3),(0,4)],5)             => 0
([(0,2),(0,3),(0,4),(4,1)],5)             => 0
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)       => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 0
([(1,3),(1,4),(4,2)],5)                   => 1
([(0,3),(0,4),(4,1),(4,2)],5)             => 1
([(1,2),(1,3),(2,4),(3,4)],5)             => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)       => 3
([(0,3),(0,4),(3,2),(4,1)],5)             => 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)       => 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 4
([(2,3),(3,4)],5)                         => 0
([(1,4),(4,2),(4,3)],5)                   => 1
([(0,4),(4,1),(4,2),(4,3)],5)             => 1
([(2,4),(3,4)],5)                         => 0
([(1,4),(2,4),(4,3)],5)                   => 1
([(0,4),(1,4),(4,2),(4,3)],5)             => 4
([(1,4),(2,4),(3,4)],5)                   => 1
([(0,4),(1,4),(2,4),(4,3)],5)             => 1
([(0,4),(1,4),(2,4),(3,4)],5)             => 0
([(0,4),(1,4),(2,3)],5)                   => 1
([(0,4),(1,3),(2,3),(2,4)],5)             => 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)       => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2
([(0,4),(1,4),(2,3),(4,2)],5)             => 4
([(0,4),(1,3),(2,3),(3,4)],5)             => 1
([(0,4),(1,4),(2,3),(2,4)],5)             => 1
([(0,4),(1,4),(2,3),(3,4)],5)             => 0
([(1,4),(2,3)],5)                         => 0
([(1,4),(2,3),(2,4)],5)                   => 0
([(0,4),(1,2),(1,4),(2,3)],5)             => 3
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)       => 3
([(1,3),(1,4),(2,3),(2,4)],5)             => 0
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)       => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 4
([(0,4),(1,2),(1,4),(4,3)],5)             => 3
([(0,4),(1,2),(1,3)],5)                   => 1
([(0,4),(1,2),(1,3),(1,4)],5)             => 1
([(0,2),(0,4),(3,1),(4,3)],5)             => 2
([(0,4),(1,2),(1,3),(3,4)],5)             => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)       => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)       => 1
([(0,3),(0,4),(1,2),(1,4)],5)             => 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)       => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)       => 4
([(0,3),(1,2),(1,4),(3,4)],5)             => 3
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)       => 4
([(1,4),(3,2),(4,3)],5)                   => 2
([(0,3),(3,4),(4,1),(4,2)],5)             => 4
([(1,4),(2,3),(3,4)],5)                   => 1
([(0,4),(1,2),(2,4),(4,3)],5)             => 3
([(0,3),(1,4),(4,2)],5)                   => 2
([(0,4),(3,2),(4,1),(4,3)],5)             => 3
([(0,4),(1,2),(2,3),(2,4)],5)             => 3
([(0,4),(2,3),(3,1),(4,2)],5)             => 4
([(0,3),(1,2),(2,4),(3,4)],5)             => 2
([(0,4),(1,2),(2,3),(3,4)],5)             => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)       => 3

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Created: Oct 09, 2020 at 18:38 by Martin Rubey

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Last Updated: Oct 09, 2020 at 18:38 by Martin Rubey