Journal of Integer Sequences, Vol. 24 (2021), Article 21.10.4

Colorful Tilings and Permutations

Jonathan Beagley and Lara Pudwell
Department of Mathematics and Statistics
Valparaiso University
Valparaiso, IN 46383


We study tilings of rectangular and circular arrays with specified sets of colored rectangular tiles. In particular, we consider rectangular tiles of arbitrarily large size, but where the number of colors available to use on a particular tile is determined by its position on the array. While tiling enumeration is often used to prove identities involving Fibonacci and Lucas numbers, the tilings we examine yield natural connections with sets of permutations.

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(Concerned with sequences A000079 A000225 A001710 A002627 A033312 A094258 A345887 A345889.)

Received June 29 2021; revised version received November 9 2021. Published in Journal of Integer Sequences, November 26 2021.

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