The boolean lattice on n elements is the poset of binary strings of length n with order given by componentwise ordering.
i1 : n = 3;
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i2 : B = booleanLattice n
o2 = B
o2 : Poset
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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
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It is also the
n-fold product of the
chain of length
2.
i4 : B == product(n, i -> chain 2)
o4 = true
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Further, it is the
divisorPoset of the product of
n distinct primes.
i5 : B == divisorPoset (2*3*5)
o5 = true
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