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

i1 : n = 5;

i2 : C = chain n

o2 = Poset{cache => CacheTable{...16...}                }
           GroundSet => {1, 2, 3, 4, 5}
           RelationMatrix => | 1 1 1 1 1 |
                             | 0 1 1 1 1 |
                             | 0 0 1 1 1 |
                             | 0 0 0 1 1 |
                             | 0 0 0 0 1 |
           Relations => {{1, 2}, {2, 3}, {3, 4}, {4, 5}}

o2 : Poset

i3 : C == poset(toList(1..n), (a,b) -> a <= b)

o3 = true

i4 : C == divisorPoset(2^(n-1))

o4 = true