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A triangular domino tiling is a tiling on a shape using triangular dominoes. …

A polydomino of size \$2n\$ is defined as a polyomino of size \$2n\$ which can be tiled with \$n\$ dominoes. The following are some examples of polydominoes for \$n=3\$ (hexominoes). . O O | . O . . … The following shape has two ways to tile with dominoes, but it is counted only once just like other hexominoes. . O O O O . O O . The sequence is OEIS 056786. …

Background A maximal domino placement (MDP) on a rectangular grid is a non-overlapping placement of zero or more dominoes, so that no more dominoes can be added without overlapping some existing domino … Alternatively, it can be thought of as a tiling using dominoes and monominoes (single square pieces) so that no two monominoes are adjacent to each other. …

Much harder than Can this pattern be made with dominoes? Challenge A grid of width \$w\$ and height \$h\$ is given, filled with 1s and 0s. … You cannot overlap dominoes. What is the maximum number of dominoes you can fit in the given grid? The worst-case time complexity should be \$\mathcal{O}(w^2h^2)\$ or lower. …

Challenge We once had a challenge to count domino tilings of m by n grid, and we all know that, for any fixed number of rows, the number of domino tilings by columns forms a linear recurrence. Then wh …

Background A saturated domino covering is a placement of dominoes over an area such that the dominoes are completely inside the area, the dominoes entirely cover the given area, the dominoes may overlap … EE. .FF Challenge Given the dimensions (width and height) of a rectangle, compute the maximum number of dominoes in its saturated domino covering. …