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

Simon Blackburn; Yinsong Chen; Vladislav Kargin

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
Publication status	Accepted/In press - 18 Apr 2025

Cite this

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title = "An upper bound on the per-tile entropy of ribbon tilings",

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.",

author = "Simon Blackburn and Yinsong Chen and Vladislav Kargin",

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AU - Chen, Yinsong

AU - Kargin, Vladislav

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N2 - 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.

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.

M3 - Article

JO - Combinatorial Theory

JF - Combinatorial Theory

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