---
bibliography:
- 'DimerReferences.bib'
title: '**Combinatorics of the Dimer Model on a Strip**'
---

ITFA-2007-41

<span style="font-variant:small-caps;">Abstract</span>\

In this note, we give a closed formula for the partition function of the dimer model living on a $2\times n$ strip of squares or hexagons on the torus for arbitrary even $n$. The result is derived in two ways, by using a Potts model like description for the dimers, and via a recursion relation that was obtained from a map to a $1D$ monomer–dimer system.

The problem of finding the number of perfect matchings can also be translated to the problem of finding a minmal feedback arc set on the dual graph.

Acknowledgements {#acknowledgements .unnumbered}
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We would like to thank Robbert Dijkgraaf for discussions. Furthermore, we would like to thank the V. Simons Workshop for Mathematics and Physics for hospitality, where this note was concluded. D.O. is supported in part by <span style="font-variant:small-caps;">INFN</span> and <span style="font-variant:small-caps;">MIUR</span> under contract 2005-024045 and by the European Community’s Human Potential Program <span style="font-variant:small-caps;">MRTN</span>-<span style="font-variant:small-caps;">CT</span>-2004-005104. S.R. is supported by the EC’s Marie Curie Research Training Network under the contract <span style="font-variant:small-caps;">MRTN</span>-<span style="font-variant:small-caps;">CT</span>-2004-512194 “Superstrings”.
