A generalization of Aztec diamond theorem, part I

2013/10/02 by Tri Lai, Lai, Tri
Computer Science · Mathematics · #05A15 #05E99 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1310.0851

openalex publication_date 2013/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize Aztec diamond theorem (N. Elkies, G. Kuperberg, M. Larsen, and J. Propp, Alternating-sign matrices and domino tilings, Journal Algebraic Combinatoric, 1992) by showing that the numbers of tilings of a certain family of regions in the square lattice with southwest-to-northeast diagonals drawn in are given by powers of 2. We present a proof for the generalization by using a bijection between domino tilings and non-intersecting lattice paths.

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