Here is a small gallery of posets produced by the package Posets.nb.
This is an diagram showing configurations
in the "chip-firing" posets studied by Bjorner, Lovasz, and Shor (add
reference). Starting with a stack of eight chips, one generates new configurations by
removing two chips from a pile and distributing them to the two adjacent positions.
This is the lattice of subsets of a
5-elements set (and of course it can also be viewed as a projection of the 2-skeleton of a
5-dimensional cube).
This is a diagram of the symmetric group
S_5, consisting of all permutations of a 5-element set, ordered by the "weak"
order. It may also be viewed as a diagram of the Cayley graph of S_5. The highlighted
elements are the Andre (alternating) permutations. (E. Hunsicker, 1992)
This is the strong order on S_4 (also known
as the Bruhat order).
This is the bottom 6 levels of an example of
a Young-Fibonacci lattice, introduced by Richard Stanley.
I will be expanding this collection. If produce
some other interesting examples with my package, please send them to me (cgreene@haverford.edu) and I will add them to
this collection.