- FindStat

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Identifier

St001679: Lattices ⟶ ℤ

Values

([],1) => 1

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

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

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

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

([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 24

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

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

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

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

([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 54

([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 52

([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 46

([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 32

([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 32

([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 32

([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 46

([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 32

([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 50

([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 40

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 48

([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 50

([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 44

([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 32

([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 44

([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 116

([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 114

([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 108

([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 94

([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 64

([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => 64

([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => 64

([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => 64

([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 94

([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => 64

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 94

([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 64

([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 64

([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 64

([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => 108

([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 94

([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 64

([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 112

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => 102

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 80

([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 110

([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => 96

([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 108

([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => 110

([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 104

([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 80

([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 100

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => 104

([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 104

([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 112

([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 106

([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 92

([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 88

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 88

([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 106

([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 92

([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 64

([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => 92

([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 64

([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => 92

([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 100

([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 100

([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 94

([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => 64

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 106

([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 88

([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 106

([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 64

([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 92

([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 64

([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 100

([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 92

([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 64

([(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) => 242

([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8) => 240

([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8) => 234

([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8) => 220

([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8) => 190

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8) => 128

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8) => 128

([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8) => 128

([(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,4),(7,6)],8) => 128

([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8) => 128

([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8) => 190

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8) => 128

([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8) => 190

([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8) => 190

([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8) => 128

([(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(5,4),(6,7)],8) => 128

([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => 128

([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8) => 128

([(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7),(7,1)],8) => 128

([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,4),(7,3)],8) => 128

([(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1),(6,4),(6,5)],8) => 128

([(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4),(6,7)],8) => 128

([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8) => 220

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Description

The number of subsets of a lattice whose meet is the bottom element.

Code

def statistic(L):
    r = 0
    b = L.bottom()
    for s in subsets(L):
        if s and L.meet(s) == b:
            r += 1
    return r

Created

Feb 08, 2021 at 13:48 by Martin Rubey

Updated

Feb 08, 2021 at 13:48 by Martin Rubey