Dimers on graphs in non-orientable surfaces

Understand

The main result of this paper is a Pfaffian formula for the partition function of the dimer model on a graph G embedded in a closed, possibly non-orientable surface S.

• This formula is suitable for computational purposes, and it is obtained using purely geometrical methods.
• The key step in the proof consists of a correspondence between some orientations on G and the set of pin^- structures on S.
• This generalizes (and simplifies) the results of a previous paper [2].