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

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 \(n-1\)...

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Bibliographic Details
Published inarXiv.org
Main Authors Blackburn, Simon, Chen, Yinsong, Kargin, Vladislav
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.08.2024
Subjects
Entropy
Upper bounds
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Summary: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.
ISSN:2331-8422