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Posets :: isLattice

isLattice -- determines if a poset is a lattice



The poset $P$ is a lattice if every pair of vertices has a unique least upper bound and a unique greatest lower bound, i.e., every pair of vertices has a unique meet and a unique join. Equivalently, the poset $P$ is a lattice if it is both a lower semilattice and an upper semilattice.

Clearly, the $n$ chain and the $n$ booleanLattice are lattices.

i1 : n = 4;
i2 : isLattice chain n

o2 = true
i3 : B = booleanLattice n;
i4 : isLattice B

o4 = true

The middle ranks of the $n$ booleanLattice are not lattices.

i5 : isLattice flagPoset(B, {1,2,3})

o5 = false

See also

Ways to use isLattice :

For the programmer

The object isLattice is a method function.