Domino Tilings of Aztec Octagons

Hyunggi Kim; Sangyop Lee; Seungsang Oh

doi:10.1007/s00373-023-02645-9

Domino Tilings of Aztec Octagons

Hyunggi Kim, Sangyop Lee, Seungsang Oh

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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
Article number	45
Journal	Graphs and Combinatorics
Volume	39
Issue number	3
DOIs	https://doi.org/10.1007/s00373-023-02645-9
Publication status	Published - 2023 Jun

Bibliographical note

Funding Information:
The second author was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2020R1F1A1A01074716). The third author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1F1A1064273).

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023.

Keywords

Aztec diamond
Delannoy path
Domino tiling
Perfect matching

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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Cite this

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AB - 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.

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Domino Tilings of Aztec Octagons

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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