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Identifier

St001095: Posets ⟶ ℤ

Values

([],2) => 1

([(0,1)],2) => 0

([],3) => 1

([(1,2)],3) => 3

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

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

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

([],4) => 1

([(2,3)],4) => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([],5) => 1

([(3,4)],5) => 4

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

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

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

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

([(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) => 9

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,4),(1,4),(2,3)],5) => 8

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

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

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

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

([(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) => 1

([(1,4),(2,3)],5) => 7

([(1,4),(2,3),(2,4)],5) => 9

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

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

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

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

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

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

([(0,4),(1,2),(1,3)],5) => 8

([(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) => 4

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

([(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) => 1

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

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

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

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

([(1,4),(3,2),(4,3)],5) => 7

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

([(1,4),(2,3),(3,4)],5) => 9

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

([(0,3),(1,4),(4,2)],5) => 11

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

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

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

([(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) => 0

([],6) => 1

([(4,5)],6) => 4

([(3,4),(3,5)],6) => 5

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

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

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

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

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

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

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

([(1,3),(1,4),(1,5),(5,2)],6) => 9

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

([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 9

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

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

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Description

The number of non-isomorphic posets with precisely one further covering relation.

Code

def statistic(P):
    H = P.hasse_diagram()
    l = set()
    for a,b in cartesian_product((P,P)):
        if a != b and not H.has_edge(a, b) and not H.has_edge(b, a):
            H.add_edge(a,b)
            try:
                Q = Poset(H, cover_relations=True)
            except ValueError:
                pass
            else:
                Q = Q.canonical_label()
                l.add(Q)
            H.delete_edge(a,b)

    return len(l)

Created

Feb 01, 2018 at 11:12 by Martin Rubey

Updated

Feb 01, 2018 at 11:12 by Martin Rubey