Some Polyomino Tilings of the Plane

We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the L tetromino, and the T tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by each of these. For the T tetromino, we also derive a lower bound from the solution of the Ising model in two dimensions.

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Cris Moore <>