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

2024/08/17 by Blackburn, Simon, Chen, Yinsong, Kargin, Vladislav
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.09272

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 log₂ n. This bound improves the best previously known bounds of n-1 for general regions, and the asymptotic upper bound of log₂ (en) for growing rectangles, due to Chen and Kargin.

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