isUpperSemilattice -- determines if a poset is an upper (or join) semilattice

Synopsis

The poset $P$ is an upper semilattice if every pair of vertices has a unique least upper bound (join).

Clearly, the $n$ chain and the $n$ booleanLattice are upper semilattices.

i1 : n = 4;

i2 : isUpperSemilattice chain n

o2 = true

i3 : B = booleanLattice n;

i4 : isUpperSemilattice B

o4 = true

The middle ranks of the $n$ booleanLattice are not upper semilattices.

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

o5 = false

However, the upper ranks of the $n$ booleanLattice are non-lattice upper semilattices.

i6 : B' = flagPoset(B, {1,2,3,4});

i7 : isLattice B'

o7 = false

i8 : isUpperSemilattice B'

o8 = true