Domino tilings of the expanded Aztec diamond

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    6 Citations (Scopus)

    Abstract

    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
    Volume341
    Issue number4
    DOIs
    Publication statusPublished - 2018 Apr

    Bibliographical note

    Publisher Copyright:
    © 2017 Elsevier B.V.

    Keywords

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

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Discrete Mathematics and Combinatorics

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