Combinatorics of the Double-Dimer Model
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Date
2020-09-24
Authors
Jenne, Helen
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Journal ISSN
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Publisher
University of Oregon
Abstract
We prove that the partition function for tripartite double-dimer configurations of a planar bipartite graph satisfies a recurrence related to the Desnanot-Jacobi identity from linear algebra. A similar identity for the dimer partition function was established nearly 20 years ago by Kuo. This work was motivated in part by the potential for applications, including a problem in Donaldson-Thomas and Pandharipande-Thomas theory, which we will discuss. The proof of our recurrence requires generalizing work of Kenyon and Wilson; specifically, lifting their assumption that the nodes of the graph be black and odd or white and even.
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Keywords
dimer model, double-dimer model