Facts about spanning trees

This page contains some facts about the number of spanning graphs in a P_n x P_m graph, which were posted to rec.puzzles by Noam Elkies. Someone posted the following question: I replied with the remark that this is equal to the number of spanning trees in a P_n x P_m graph, and pointed to my results.

Noam Elkies, however, gave the following reply:

And then posted the next follow-up: I send him the following question by email: And he replied with:

home and email