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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