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.
Keywords
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}
}
Comments
15 pages