- FindStat

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Identifier

St000641: Posets ⟶ ℤ

Values

([],2) => 2

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

([],3) => 3

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

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

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

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

([],4) => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([],5) => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([],6) => 6

([(4,5)],6) => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of non-empty boolean intervals in a poset.

References

[1] Samuel, M. Number of Boolean algebra subintervals in weak order of $S_n$ MathOverflow:253773

Code

def statistic(P):
    l = [P.subposet(P.interval(a,b)) for a,b in P.relations()]
    count = 0
    for Q in l:
        try:
            Q = LatticePoset(Q)
        except ValueError:
            continue
        else:
            try:
                k = ZZ(log_b(Q.cardinality(), 2))
            except TypeError:
                continue
            else:
                if Q.is_isomorphic(posets.BooleanLattice(k)):
                    count += 1
    return count

Created

Nov 03, 2016 at 06:40 by Martin Rubey

Updated

Nov 03, 2016 at 09:57 by Martin Rubey