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Generating function of the tilings of Aztec rectangle with holes

Combinatorics 2015-04-02 v6

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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Cite

@article{arxiv.1402.0825,
  title  = {Generating function of the tilings of Aztec rectangle with holes},
  author = {Tri Lai},
  journal= {arXiv preprint arXiv:1402.0825},
  year   = {2015}
}

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15 pages