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arXiv · 2408.09272

An upper bound on the per-tile entropy of ribbon tilings

Simon Blackburn·Yinsong Chen·Vladislav Kargin
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Abstract

This paper considers $n$-ribbon tilings of general regions and their per-tile entropy (the binary logarithm of the number of tilings divided by the number of tiles). We show that the per-tile entropy is bounded above by $\log_2 n$. This bound improves the best previously known bounds of $n-1$ for general regions, and the asymptotic upper bound of $\log_2 (en)$ for growing rectangles, due to Chen and Kargin.

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Simon Blackburn, Yinsong Chen, Vladislav Kargin. 2024-12-06. An upper bound on the per-tile entropy of ribbon tilings. https://arxiv.org/abs/2408.09272

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