Domino Tilings of Aztec Octagons

Hyunggi Kim, Sangyop Lee, Seungsang Oh

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number45
JournalGraphs and Combinatorics
Issue number3
Publication statusPublished - 2023 Jun


  • Aztec diamond
  • Delannoy path
  • Domino tiling
  • Perfect matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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