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 |
The object booleanLattice is a method function.