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arXiv · 1309.0268

Laurent biorthogonal polynomials, q-Narayana polynomials and domino tilings of the Aztec diamonds

Shuhei Kamioka
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Abstract

A Töplitz determinant whose entries are described by a q-analogue of the Narayana polynomials is evaluated by means of Laurent biorthogonal polynomials which allow of a combinatorial interpretation in terms of Schröder paths. As an application, a new proof is given to the Aztec diamond theorem by Elkies, Kuperberg, Larsen and Propp concerning domino tilings of the Aztec diamonds. The proof is based on the correspondence with non-intersecting Schröder paths developed by Eu and Fu.

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Shuhei Kamioka. 2013-09-01. Laurent biorthogonal polynomials, q-Narayana polynomials and domino tilings of the Aztec diamonds. https://arxiv.org/abs/1309.0268

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