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

摘要

A T\"oplitz determinant whose entries are described by a q-analogue of theNarayana polynomials is evaluated by means of Laurent biorthogonal polynomialswhich allow of a combinatorial interpretation in terms of Schr\"oder paths. Asan 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 Schr\"oder pathsdeveloped by Eu and Fu.