Values
=>
Cc0029;cc-rep
([],1)=>0
([(0,1)],2)=>0
([(0,2),(2,1)],3)=>0
([(0,1),(0,2),(1,3),(2,3)],4)=>2
([(0,3),(2,1),(3,2)],4)=>0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>3
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>0
([(0,4),(2,3),(3,1),(4,2)],5)=>0
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>4
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>4
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>4
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>0
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>0
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>0
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>4
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>3
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>4
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>3
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>0
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>3
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>5
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>5
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>5
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>0
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>0
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)=>0
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>0
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>5
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>0
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>5
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>0
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>0
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>0
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)=>5
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>5
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>0
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>5
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)=>5
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>5
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>3
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>4
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)=>5
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>5
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>4
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)=>4
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>4
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)=>5
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)=>5
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>4
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>3
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>5
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>4
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>0
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>4
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>0
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>4
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>4
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>4
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>5
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>0
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)=>5
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>3
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>5
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>0
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>4
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>0
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>4
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>4
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>0
([],0)=>0
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Description
The number of zero divisors in a lattice.
Let $0$ be the bottom element of a lattice. A zero divisor of a lattice is an element $a\neq 0$ such that there is another element $b\neq 0$ with $a\wedge b = 0$.
Let $0$ be the bottom element of a lattice. A zero divisor of a lattice is an element $a\neq 0$ such that there is another element $b\neq 0$ with $a\wedge b = 0$.
References
[1] Lu, D., Wu, T. The zero-divisor graphs of posets and an application to semigroups MathSciNet:2729023
[2] Halaš, Radomír, Jukl, M. On Beck's coloring of posets MathSciNet:2519197
[2] Halaš, Radomír, Jukl, M. On Beck's coloring of posets MathSciNet:2519197
Code
def statistic(L):
z = L.bottom()
non_bottom = [a for a in L if a != z]
return sum(1 for a in non_bottom if any(L.meet(a, b) == z for b in non_bottom))
Created
Dec 01, 2025 at 11:41 by Martin Rubey
Updated
Dec 01, 2025 at 11:41 by Martin Rubey
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