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arXiv · 2408.10331

Revisiting Dice Relabeling using Cyclotomic Polynomials

Yikai Chao·Josh Gabel·Carlye Larson·George David Nasr
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Abstract

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.

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Yikai Chao, Josh Gabel, Carlye Larson, George David Nasr. 2024-08-19. Revisiting Dice Relabeling using Cyclotomic Polynomials. https://arxiv.org/abs/2408.10331

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