Domino tilings of the Aztec Diamond

Snapshots of modern mathematics from Oberwolfach

Domino tilings of the Aztec Diamond

Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with dominoes?

One specific paper cutout can be mathematically described as the so-called Aztec Diamond, and a way to cover it with dominoes is a domino tiling.

In this snapshot we revisit some of the seminal combinatorial ideas used to enumerate the number of domino tilings of the Aztec Diamond. The existing connection with the study of the so-called alternating-sign matrices is also explored.

If you are interested in translating this Snapshot, please contact us at

Mathematical subjects

Discrete Mathematics and Foundations
Probability Theory and Statistics


Juanjo Rué


DOI (Digital Object Identifier)


Download PDF


snapshots: overview

Mathematical subjects

Algebra and Number Theory
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Humanities and Social Sciences
Life Science
Reflections on Mathematics

These icons are available under the CC BY-SA 4.0 license. Please feel free to use them to classify your own content.
The vector icons can be downloaded here.