Abstract
Considerable energy has been devoted to understanding domino tilings: for example, Elkies, Kuperberg, Larsen and Propp proved the Aztec diamond theorem, which states that the number of domino tilings for the Aztec diamond of order n is equal to 2 n(n+1)/2, and the authors recently counted the number of domino tilings for augmented Aztec rectangles and their chains by using Delannoy paths. In this paper, we count domino tilings for two new shapes of regions, bounded augmented Aztec rectangles and Aztec octagons by constructing a bijection between domino tilings for these regions and the associated generalized Motzkin paths.
Original language | English |
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Article number | 45 |
Journal | Graphs and Combinatorics |
Volume | 39 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2023 Jun |
Keywords
- Aztec diamond
- Delannoy path
- Domino tiling
- Perfect matching
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics