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

## Synopsis

• Usage:
B = booleanLattice n
• Inputs:
• Outputs:
• B, an instance of the type Poset,

## 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

• chain -- generates the chain poset on $n$ elements