English

Universal cycles for permutations

Combinatorics 2007-10-31 v1

Abstract

A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1 distinct integers are used. This is best possible and proves a conjecture of Chung, Diaconis and Graham.

Keywords

Cite

@article{arxiv.0710.5611,
  title  = {Universal cycles for permutations},
  author = {J. Robert Johnson},
  journal= {arXiv preprint arXiv:0710.5611},
  year   = {2007}
}

Comments

14 pages, 2 figures

R2 v1 2026-06-21T09:37:53.021Z