---
tag: 83PJCPB9VA
kind: concept
name: Domino tiling
msc: [05B45, 05C70, 52C20]
specializes: [GKJK293DXS]
sources:
  - url: https://en.wikipedia.org/wiki/Domino_tiling
same_as:
  wikidata: Q21042776
  wikipedia: Domino tiling
---

## Summary

A domino tiling of a region made of unit squares is a covering of it by non-overlapping $1 \times 2$ and $2 \times 1$ rectangles.
Domino tilings are the same as [[perfect matchings|0NHK9MFFW9]] of the grid graph of the cells.
Counting them is a classical problem of combinatorics and statistical physics, solved for rectangles by Kasteleyn and by Temperley and Fisher in 1961.

## Explanations

### L1 human

Take a chessboard and a box of dominoes, each covering exactly two neighbouring squares.
A domino tiling places dominoes so that every square is covered exactly once.
A $2 \times 2$ board has two tilings: two horizontal dominoes or two vertical ones.
The ordinary $8 \times 8$ chessboard has $12{,}988{,}816$ domino tilings.