Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001651
Mapping
St001651: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => 0
([(0,2),(2,1)],3)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
([(0,3),(2,1),(3,2)],4)
 => 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 3
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 4
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 4
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => 4
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 4
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 4
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 3
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => 3
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => 3
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
 => 3
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
 => 3
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => 3
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
 => 3
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => 5
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
 => 3
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => 3
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => 5
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => 3
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => 3
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 3
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => 3
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => 3
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => 3
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 3
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => 3
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => 5
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => 5
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => 5
Description
The Frankl number of a lattice. For a lattice $L$ on at least two elements, this is $$ \max_x(|L|-2|[x, 1]|), $$ where we maximize over all join irreducible elements and $[x, 1]$ denotes the interval from $x$ to the top element. Frankl's conjecture asserts that this number is non-negative, and zero if and only if $L$ is a Boolean lattice.