Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 1039-1054 |
| Number of pages | 16 |
| Journal | Graphs and Combinatorics |
| Volume | 32 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 1 2016 |
Bibliographical note
Publisher Copyright:© 2015, Springer Japan.
Keywords
- Aztec diamonds
- Aztec rectangles
- Dual graph
- Perfect matchings
- Tilings