- FindStat

Identifier

St001637: Posets ⟶ ℤ

Values

=>
                            Cc0014;cc-rep
                            
                            
                            

                        ([],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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Description

The number of (upper) dissectors of a poset.

References

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

Code

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

Created

Oct 09, 2020 at 18:38 by Martin Rubey

Updated

Oct 09, 2020 at 18:38 by Martin Rubey