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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.09272 |
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| _version_ | 1866916510510874624 |
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| author | Blackburn, Simon Chen, Yinsong Kargin, Vladislav |
| author_facet | Blackburn, Simon Chen, Yinsong Kargin, Vladislav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An upper bound on the per-tile entropy of ribbon tilings Blackburn, Simon Chen, Yinsong Kargin, Vladislav Combinatorics 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. |
| title | An upper bound on the per-tile entropy of ribbon tilings |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.09272 |