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Posets :: booleanLattice

booleanLattice -- generates the boolean lattice on $n$ elements

Synopsis

Description

The boolean lattice on n elements is the poset of binary strings of length n with order given by componentwise ordering.
i1 : n = 3;
i2 : B = booleanLattice n

o2 = B

o2 : Poset
It can also be seen as the poset of subsets of a set of n elements with order given by containment.
i3 : B == poset(subsets n, isSubset)

o3 = true
It is also the n-fold product of the chain of length 2.
i4 : B == product(n, i -> chain 2)

o4 = true
Further, it is the divisorPoset of the product of n distinct primes.
i5 : B == divisorPoset (2*3*5)

o5 = true

See also

Ways to use booleanLattice :