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arXiv · 2311.13072

Counting tilings of the $n \times m$ grid, cylinder, and torus

Peter Kagey·William Keehn
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Abstract

We count tilings of the $n \times m$ rectangular grid, cylinder, and torus with arbitrary tile sets up to arbitrary symmetries of the square and rectangle, along with cyclic shifting of rows and columns. This provides a unifying framework for understanding a family of counting problems, expanding on the work by Ethier and Lee counting tilings of the torus by tiles of two colors.

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Peter Kagey, William Keehn. 2023-12-22. Counting tilings of the $n \times m$ grid, cylinder, and torus. https://arxiv.org/abs/2311.13072

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