English

A Direct Construction of Non-Transitive Dice Sets

Combinatorics 2016-10-28 v1 Probability

Abstract

In this paper, we give a direct construction for a set of dice realizing any given tournament TT. The construction for a tournament with nn vertices requires a number of sides on the order of nn, which appears to be the best general construction to date. Our construction relies only on a standard theorem from graph theory.

Keywords

Cite

@article{arxiv.1610.08595,
  title  = {A Direct Construction of Non-Transitive Dice Sets},
  author = {Levi Angel and Matt Davis},
  journal= {arXiv preprint arXiv:1610.08595},
  year   = {2016}
}
R2 v1 2026-06-22T16:33:21.358Z