Generating Function of the Tilings of an Aztec Rectangle with Holes

Tri Lai

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider a generating function of the domino tilings of an Aztec rectangle with several unit squares removed from the boundary. 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.

Original languageEnglish (US)
Pages (from-to)1039-1054
Number of pages16
JournalGraphs and Combinatorics
Issue number3
StatePublished - May 1 2016

Bibliographical note

Funding Information:
This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation (Grant no. DMS-0931945). The author would like to thank the anonymous referee for his careful reading and helpful comments.

Publisher Copyright:
© 2015, Springer Japan.


  • Aztec diamonds
  • Aztec rectangles
  • Dual graph
  • Perfect matchings
  • Tilings


Dive into the research topics of 'Generating Function of the Tilings of an Aztec Rectangle with Holes'. Together they form a unique fingerprint.

Cite this