- FindStat

Identifier

St000327: Posets ⟶ ℤ

Values

([],2) => 0
([(0,1)],2) => 1
([],3) => 0
([(1,2)],3) => 1
([(0,1),(0,2)],3) => 2
([(0,2),(2,1)],3) => 2
([(0,2),(1,2)],3) => 2
([],4) => 0
([(2,3)],4) => 1
([(1,2),(1,3)],4) => 2
([(0,1),(0,2),(0,3)],4) => 3
([(0,2),(0,3),(3,1)],4) => 3
([(0,1),(0,2),(1,3),(2,3)],4) => 4
([(1,2),(2,3)],4) => 2
([(0,3),(3,1),(3,2)],4) => 3
([(1,3),(2,3)],4) => 2
([(0,3),(1,3),(3,2)],4) => 3
([(0,3),(1,3),(2,3)],4) => 3
([(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) => 3
([],5) => 0
([(3,4)],5) => 1
([(2,3),(2,4)],5) => 2
([(1,2),(1,3),(1,4)],5) => 3
([(0,1),(0,2),(0,3),(0,4)],5) => 4
([(0,2),(0,3),(0,4),(4,1)],5) => 4
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 5
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 6
([(1,3),(1,4),(4,2)],5) => 3
([(0,3),(0,4),(4,1),(4,2)],5) => 4
([(1,2),(1,3),(2,4),(3,4)],5) => 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 5
([(0,3),(0,4),(3,2),(4,1)],5) => 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 6
([(2,3),(3,4)],5) => 2
([(1,4),(4,2),(4,3)],5) => 3
([(0,4),(4,1),(4,2),(4,3)],5) => 4
([(2,4),(3,4)],5) => 2
([(1,4),(2,4),(4,3)],5) => 3
([(0,4),(1,4),(4,2),(4,3)],5) => 4
([(1,4),(2,4),(3,4)],5) => 3
([(0,4),(1,4),(2,4),(4,3)],5) => 4
([(0,4),(1,4),(2,4),(3,4)],5) => 4
([(0,4),(1,4),(2,3)],5) => 3
([(0,4),(1,3),(2,3),(2,4)],5) => 4
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 5
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 6
([(0,4),(1,4),(2,3),(4,2)],5) => 4
([(0,4),(1,3),(2,3),(3,4)],5) => 4
([(0,4),(1,4),(2,3),(2,4)],5) => 4
([(0,4),(1,4),(2,3),(3,4)],5) => 4
([(1,4),(2,3)],5) => 2
([(1,4),(2,3),(2,4)],5) => 3
([(0,4),(1,2),(1,4),(2,3)],5) => 4
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5
([(1,3),(1,4),(2,3),(2,4)],5) => 4
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 5
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 6
([(0,4),(1,2),(1,4),(4,3)],5) => 4
([(0,4),(1,2),(1,3)],5) => 3
([(0,4),(1,2),(1,3),(1,4)],5) => 4
([(0,2),(0,4),(3,1),(4,3)],5) => 4
([(0,4),(1,2),(1,3),(3,4)],5) => 4
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 5
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 5
([(0,3),(0,4),(1,2),(1,4)],5) => 4
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 5
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 6
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 5
([(0,3),(1,2),(1,4),(3,4)],5) => 4
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 5
([(1,4),(3,2),(4,3)],5) => 3
([(0,3),(3,4),(4,1),(4,2)],5) => 4
([(1,4),(2,3),(3,4)],5) => 3
([(0,4),(1,2),(2,4),(4,3)],5) => 4
([(0,3),(1,4),(4,2)],5) => 3
([(0,4),(3,2),(4,1),(4,3)],5) => 4
([(0,4),(1,2),(2,3),(2,4)],5) => 4
([(0,4),(2,3),(3,1),(4,2)],5) => 4
([(0,3),(1,2),(2,4),(3,4)],5) => 4
([(0,4),(1,2),(2,3),(3,4)],5) => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 5

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$F_{2} = 1 + q$

$F_{3} = 1 + q + 3\ q^{2}$

$F_{4} = 1 + q + 4\ q^{2} + 8\ q^{3} + 2\ q^{4}$

$F_{5} = 1 + q + 4\ q^{2} + 11\ q^{3} + 29\ q^{4} + 12\ q^{5} + 5\ q^{6}$

Description

The number of cover relations in a poset.
Equivalently, this is also the number of edges in the Hasse diagram [1].

References

[1] wikipedia:Hasse_diagram

Code

def statistic(P):
    return len(P.cover_relations())

Created

Dec 13, 2015 at 01:36 by Daniel Shira

Updated

Dec 13, 2015 at 07:44 by Christian Stump