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 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.