Domino Tilings of Aztec Octagons
- Authors
- Kim, H.; Lee, S.; Oh, S.
- Issue Date
- Jun-2023
- Publisher
- Springer
- Keywords
- Aztec diamond; Delannoy path; Domino tiling; Perfect matching
- Citation
- Graphs and Combinatorics, v.39, no.3
- Journal Title
- Graphs and Combinatorics
- Volume
- 39
- Number
- 3
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/74281
- DOI
- 10.1007/s00373-023-02645-9
- ISSN
- 0911-0119
1435-5914
- 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. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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