PreprintCC BY 4.0arXiv
General Constructions of Permutation-Fair Dice
Abstract
Suppose that each of n players rolls a different die and the players are ordered by their rolls. Can the dice use disjoint labels such that ties are impossible, while all n! orders remain equally likely? We give two general constructions of such dice and solve some related problems.
Related
- General constructions of normal bent partitions related to vectorial dual-bent functions
- Discrete differential-geometric Poisson brackets: general theory and explicit constructions
- On the number of $2$-dice games with prime power dice-size
- Computer-Assisted Results for n-Sided Non-Transitive Dice Taking Face Values in [n]
- Dice enterprises and polynomial approximation: uniform query tails
BibTeX
@misc{gavenciak2026general,
title = {{General Constructions of Permutation-Fair Dice}},
author = {Tomáš Gavenčiak and Bernhard Haeupler and Václav Rozhoň},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15421},
eprint = {2610.15421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15421},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - General Constructions of Permutation-Fair Dice
AU - Tomáš Gavenčiak
AU - Bernhard Haeupler
AU - Václav Rozhoň
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15421
UR - https://arxiv.org/abs/2610.15421
AB - Suppose that each of n players rolls a different die and the players are ordered by their rolls. Can the dice use disjoint labels such that ties are impossible, while all n! orders remain equally likely? We give two general constructions of such dice and solve some related problems.
ER -