A new simple proof of the Aztec diamond theorem

TL;DR

This paper presents a new, simplified proof of the Aztec diamond theorem, which counts domino tilings of a specific lattice shape, providing a more accessible understanding of this combinatorial result.

Contribution

The paper introduces a novel, simplified proof of the Aztec diamond theorem, enhancing comprehension and accessibility compared to the original proof.

Findings

The number of domino tilings of the Aztec diamond is 2^{n(n+1)/2}.

The new proof simplifies the understanding of the combinatorial structure.

The proof offers a more straightforward approach than previous methods.

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, Kuperberg, Larsen and Propp in 1992. We give a new simple proof of this theorem.