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arXiv · 1402.0825

Generating function of the tilings of Aztec rectangle with holes

Tri Lai
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Abstract

We consider a generating function of the domino tilings of an Aztec rectangle with several boundary unit squares removed. Our generating function involves two statistics: the rank of the tiling and half number of vertical dominoes as in the Aztec diamond theorem by Elkies, Kuperberg, Larsen and Propp. In addition, our work deduces a combinatorial explanation for an interesting connection between the number of lozenge tilings of a semihexagon and the number of domino tilings of an Aztec rectangle.

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Tri Lai. 2015-04-01. Generating function of the tilings of Aztec rectangle with holes. https://arxiv.org/abs/1402.0825

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