All Tilings and Board Coverings

This group gathers theorems about covering a board or a region exactly with tiles, and about the existence and counting of such tilings. It covers domino tilings of a chessboard, including the mutilated chessboard problem posed by Max Black in 1946 and the result that, after any two squares are removed, the rest can be tiled by dominoes if and only if the removed squares are of different colors, and it extends to the tilings of larger regions such as the Aztec diamond. Tilings of the plane by shapes studied as geometry belong with Geometry instead.