Dimers on surface graphs and spin structures. I

David Cimasoni; Nicolai Reshetikhin

Dimers on surface graphs and spin structures. I

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arxiv math-ph/0608070 v2 pith:KFEKKBUZ submitted 2006-08-31 math-ph math.GTmath.MP

Dimers on surface graphs and spin structures. I

David Cimasoni , Nicolai Reshetikhin This is my paper

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keywords dimersspinstructuresalternatingclosedcoefficientsdiscreteformula

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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.

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Fun with Graph States: Nonlocal Bell Pairs and the Arf Invariant
quant-ph 2026-06 unverdicted novelty 7.0

Graph-state inner products are governed by the F2-rank of the adjacency matrix and the Arf invariant, yielding a nonlocal Bell-pair factorization of the Hilbert space.