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Posets :: booleanLattice

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



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 :

For the programmer

The object booleanLattice is a method function.