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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2408.10331 |
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| _version_ | 1866917860639506432 |
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| author | Chao, Yikai Gabel, Josh Larson, Carlye Nasr, George David |
| author_facet | Chao, Yikai Gabel, Josh Larson, Carlye Nasr, George David |
| contents | We continue the exploration of a question of dice relabeling posed by Gallian and Rusin: Given $n$ dice, each labeled 1 through $m$, how many ways are there to relabel the dice without changing the frequencies of the possible sums? We answer this question in the case where $n = 2$ and $m$ is a product of three prime numbers. We also explore more general questions. We find a method for decomposing two $m$-sided dice into two dice of different sizes and give some preliminary results on relabeling two dice of different sizes. Finally, we refine a result of the aforementioned authors in the case where m is a prime power. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting Dice Relabeling using Cyclotomic Polynomials Chao, Yikai Gabel, Josh Larson, Carlye Nasr, George David Combinatorics 05A15 (Primary), 05A19 (Secondary) We continue the exploration of a question of dice relabeling posed by Gallian and Rusin: Given $n$ dice, each labeled 1 through $m$, how many ways are there to relabel the dice without changing the frequencies of the possible sums? We answer this question in the case where $n = 2$ and $m$ is a product of three prime numbers. We also explore more general questions. We find a method for decomposing two $m$-sided dice into two dice of different sizes and give some preliminary results on relabeling two dice of different sizes. Finally, we refine a result of the aforementioned authors in the case where m is a prime power. |
| title | Revisiting Dice Relabeling using Cyclotomic Polynomials |
| topic | Combinatorics 05A15 (Primary), 05A19 (Secondary) |
| url | https://arxiv.org/abs/2408.10331 |