PreprintCC BY 4.0arXiv
On the number of $2$-dice games with prime power dice-size
Abstract
We have two dices which have n labels. We want to assign a pair of labelings with positive integers to them such that the sums of the labels on them are the same and have the same distribution as at the standard labeling. We call such a pair of labelings a (dice) game of size $2$ (with dice size m). Here we give a lower and an upper bound for the dice games of size $2$ with Sicherman dice of dice size pk where p is a prime. We use the standard technique of generating polynomials to prove a non-closed combinatorial formula.
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BibTeX
@misc{seress2026number,
title = {{On the number of $2$-dice games with prime power dice-size}},
author = {Daniel Seress},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27983},
eprint = {2608.27983},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27983},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the number of $2$-dice games with prime power dice-size
AU - Daniel Seress
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27983
UR - https://arxiv.org/abs/2608.27983
AB - We have two dices which have n labels. We want to assign a pair of labelings with positive integers to them such that the sums of the labels on them are the same and have the same distribution as at the standard labeling. We call such a pair of labelings a (dice) game of size $2$ (with dice size m). Here we give a lower and an upper bound for the dice games of size $2$ with Sicherman dice of dice size p^k where p is a prime. We use the standard technique of generating polynomials to prove a non-closed combinatorial formula.
ER -