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Coupling functions for domino tilings of Aztec diamonds

Chhita, Sunil; Young, Benjamin

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Authors

Benjamin Young



Abstract

The inverse Kasteleyn matrix of a bipartite graph holds much information about the perfect matchings of the system such as local statistics which can be used to compute local and global asymptotics. In this paper, we consider three different weightings of domino tilings of the Aztec diamond and show using recurrence relations, that we can compute the inverse Kasteleyn matrix. These weights are the one-periodic weighting where the horizontal edges have one weight and the vertical edges have another weight, the qvol weighting which corresponds to multiplying the product of tile weights by q if we add a ‘box’ to the height function and the two-periodic weighting which exhibits a flat region with defects in the center.

Citation

Chhita, S., & Young, B. (2014). Coupling functions for domino tilings of Aztec diamonds. Advances in Mathematics, 259, 173-251. https://doi.org/10.1016/j.aim.2014.01.023

Journal Article Type Article
Acceptance Date Jan 21, 2014
Online Publication Date Apr 3, 2014
Publication Date Apr 3, 2014
Deposit Date Oct 12, 2016
Publicly Available Date Nov 23, 2016
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 259
Pages 173-251
DOI https://doi.org/10.1016/j.aim.2014.01.023

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