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

Simon Blackburn; Yinsong Chen; Vladislav Kargin

doi:10.5070/C65365562

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

Simon Blackburn
, Yinsong Chen
, Vladislav Kargin

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Combinatorial Theory
Volume	5
Issue number	3
DOIs	https://doi.org/10.5070/C65365562
Publication status	Published - 15 Sept 2025

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10.5070/C65365562Licence: CC BY

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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 \$\textbackslash{}log\_2 n\$. This bound improves the best previously known bounds of \$n-1\$ for general regions, and the asymptotic upper bound of \$\textbackslash{}log\_2 (en)\$ for growing rectangles, due to Chen and Kargin.",

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AB - 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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