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Mathematics > Combinatorics

arXiv:0709.1546 (math)
[Submitted on 11 Sep 2007]

Title:Combinatorics of the Dimer Model on a Strip

Authors:D.Orlando, S.Reffert
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Abstract: In this note, we give a closed formula for the partition function of the dimer model living on a (2 x 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.
Comments: 19 pages, 12 figures
Subjects: Combinatorics (math.CO); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)
Cite as: arXiv:0709.1546 [math.CO]
  (or arXiv:0709.1546v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.0709.1546

Submission history

From: Domenico Orlando [view email]
[v1] Tue, 11 Sep 2007 08:34:38 UTC (211 KB)
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