Details

Snapshot 1: considering the permutations of , for example, the number of permutations at each level corresponds to the coefficients of in the expansion of

Snapshot 2: for graphs with large numbers of vertices, clearing the "show insets" option can better show the overall structure of the lattice

Snapshot 3: other visualizations are available by changing the "graph type" option

References

[1] R. P. Stanley, Enumerative Combinatorics, Vol. 1, Cambridge: Cambridge University Press, 1997.

[2] Sequence A008302 in N. J. A. Sloane, ed., The On-Line Encyclopedia of Integer Sequences, 2008.