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.
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