Domino tilings of the expanded Aztec diamond

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5 Citations (Scopus)


The expanded Aztec diamond is a generalized version of the Aztec diamond, with an arbitrary number of long columns and long rows in the middle. In this paper, we count the number of domino tilings of the expanded Aztec diamond. The exact number of domino tilings is given by recurrence relations of state matrices by virtue of the state matrix recursion algorithm, recently developed by the author to solve various two-dimensional regular lattice model enumeration problems.

Original languageEnglish
Pages (from-to)1185-1191
Number of pages7
JournalDiscrete Mathematics
Issue number4
Publication statusPublished - 2018 Apr

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. NRF-2017R1A2B2007216 ).

Publisher Copyright:
© 2017 Elsevier B.V.


  • Aztec diamond
  • Dimer covering
  • Domino tiling
  • Perfect matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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