Abstract
The Aztec diamond of order n is the union of lattice squares in the plane intersecting the square \(|x|+|y|<n\). The Aztec diamond theorem states that the number of domino tilings of this shape is \(2^{n(n+1)/2}\). It was first proved by Elkies et al. (J. Algebraic Comb. 1(2):111–132, 1992). We give a new simple proof of this theorem.
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Notes
Note that the field of arrows is always defined on all of \(A_{n+1}\), even for a tiling of \(A_n\).
In this correspondence, the nodes in this paper correspond to odd vertices in [4].
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Fendler, M., Grieser, D. A New Simple Proof of the Aztec Diamond Theorem. Graphs and Combinatorics 32, 1389–1395 (2016). https://doi.org/10.1007/s00373-015-1663-x
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DOI: https://doi.org/10.1007/s00373-015-1663-x