Dimers on surface graphs and spin structures. I
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Abstract
Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.Keywords
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This publication has 10 references indexed in Scilit:
- Dimers and amoebaeAnnals of Mathematics, 2006
- Planar dimers and Harnack curvesDuke Mathematical Journal, 2006
- The Laplacian and Dirac operators on critical planar graphsInventiones Mathematicae, 2002
- Dimers and the Critical Ising Model on lattices of genus >1Nuclear Physics B, 2002
- Discrete Riemann Surfaces and the Ising ModelCommunications in Mathematical Physics, 2001
- A variational principle for domino tilingsJournal of the American Mathematical Society, 2000
- Matchings in Graphs on Non-orientable SurfacesJournal of Combinatorial Theory, Series B, 2000
- On the Theory of Pfaffian Orientations. I. Perfect Matchings and PermanentsThe Electronic Journal of Combinatorics, 1998
- Bosonization on higher genus Riemann surfacesCommunications in Mathematical Physics, 1987
- Spin Structures and Quadratic forms on SurfacesJournal of the London Mathematical Society, 1980