- FindStat

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Identifier

St001666: Lattices ⟶ ℤ

Values

([],1) => 2

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

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

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

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

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

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 7

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 7

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

([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 7

([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 7

([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 9

([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 10

([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 9

([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 10

([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 10

([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 9

([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 9

([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 10

([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 9

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 9

([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 8

([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10

([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7

([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 10

([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 8

([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 11

([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 13

([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 13

([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 11

([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => 14

([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => 16

([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => 14

([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 15

([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => 15

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 16

([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 13

([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 12

([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 15

([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => 12

([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 14

([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 12

([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 13

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => 14

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 12

([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 13

([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => 12

([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 11

([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => 13

([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 14

([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 11

([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 15

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => 15

([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 14

([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 11

([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 15

([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 15

([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 15

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 15

([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 13

([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 15

([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 13

([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => 17

([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 15

([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => 16

([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 14

([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 15

([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 11

([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => 11

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 15

([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 13

([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 11

([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 13

([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 15

([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 8

([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 12

([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 13

([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 13

([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 9

([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8) => 13

([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8) => 16

([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8) => 17

([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8) => 16

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8) => 13

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8) => 18

([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8) => 22

([(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,4),(7,6)],8) => 22

([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8) => 18

([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8) => 21

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8) => 21

([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8) => 25

([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8) => 23

([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8) => 19

([(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(5,4),(6,7)],8) => 22

([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => 23

([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8) => 25

([(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7),(7,1)],8) => 25

([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,4),(7,3)],8) => 23

([(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1),(6,4),(6,5)],8) => 18

([(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4),(6,7)],8) => 25

([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8) => 20

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Description

The number of non-isomorphic subposets of a lattice which are lattices.

Code

@cached_function
def subposets(P):
    if not P.cardinality():
        return P.subposet([])
    l = []
    for s in Subsets(P, P.cardinality()-1):
        Q = P.subposet(s).canonical_label()
        if Q not in l:
            l.append(Q)
        for R in subposets(Q):
            if R not in l:
                l.append(R)
    return l

def statistic(P):
    return 1+sum(1 for Q in subposets(P) if Q.is_lattice())

Created

Jan 05, 2021 at 14:02 by Martin Rubey

Updated

Feb 08, 2021 at 23:44 by Martin Rubey