English

On shortening u-cycles and u-words for permutations

Combinatorics 2018-11-01 v2

Abstract

This paper initiates the study of shortening universal cycles (u-cycles) and universal words (u-words) for permutations either by using incomparable elements, or by using non-deterministic symbols. The latter approach is similar in nature to the recent relevant studies for the de Bruijn sequences. A particular result we obtain in this paper is that u-words for nn-permutations exist of lengths n!+(1k)(n1)n!+(1-k)(n-1) for k=0,1,,(n2)!k=0,1,\ldots,(n-2)!.

Keywords

Cite

@article{arxiv.1707.06110,
  title  = {On shortening u-cycles and u-words for permutations},
  author = {Sergey Kitaev and Vladimir N. Potapov and Vincent Vajnovszki},
  journal= {arXiv preprint arXiv:1707.06110},
  year   = {2018}
}
R2 v1 2026-06-22T20:51:45.289Z