15
votes
0answers
432 views

Monomer-Dimer tatami tilings need better relationships with other math. Summary of results.

A monomer-dimer tiling of a rectangular grid with $r$ rows and $c$ columns satisfies the \emph{tatami} condition if no four tiles meet at any point. (or you can think of it as the removal of a ...
20
votes
1answer
711 views

A strange sum over bipartite graphs

While mucking around with some generating functions related to enumeration of regular bipartite graphs, I stumbled across the following cutie. I wonder if anyone has seen it before, and/or if anyone ...
1
vote
1answer
638 views

Infinite graphs as functional operators

Original Question Consider an infinite tree of constant degree $k$. For such a tree we can consider the total number of nodes at depth $n$, $g(f)$, and the total number of paths from the root, ...