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arXiv:1402.0825 [math.CO]AbstractReferencesReviewsResources

Generating function of the tilings of Aztec rectangle with holes

Tri Lai

Published 2014-02-04, updated 2015-04-01Version 6

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.

Comments: 15 pages
Categories: math.CO
Subjects: 05A15, 05E99, 05B45
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