Counting tilings of the n × m grid, cylinder, and torus

2023/11/22 by Kagey, Peter, Keehn, William
#05A05 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2311.13072

Abstract

We count tilings of the n × 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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