Squishing Dimers on the Hexagon Lattice

In this paper, we will describe and use a novel technique called “squishing”, which one applies to the dimer model on the regular honeycomb lattice. We developed this technique as an attempt to verify a conjectured generating function which arises in algebraic geometry (specifically, in the Donaldson-Thomas theory of the orbifold C/Z2 × Z2 [1]). Our attempt was only partially successful, and we were later able to compute the generating function by other means. However, the technique is interesting in of itself, being one of relatively few dimer model techniques which exploits the self-similarity of the lattice at different scales. We begin by describing the original motivation for this work.