Universal Cycles of Restricted Classes of Words

Arielle Leitner; Anant Godbole

Universal Cycles of Restricted Classes of Words

Combinatorics 2012-04-12 v2

Authors: Arielle Leitner , Anant Godbole

Abstract

It is well known that Universal Cycles of $k$ -letter words on an $n$ -letter alphabet exist for all $k$ and $n$ . In this paper, we prove that Universal Cycles exist for restricted classes of words, including: non-bijections, equitable words (under suitable restrictions), ranked permutations, and "passwords".

Keywords

universal cycles restricted words non-bijections equitable words ranked permutations passwords

Cite

@article{arxiv.0808.1309,
  title  = {Universal Cycles of Restricted Classes of Words},
  author = {Arielle Leitner and Anant Godbole},
  journal= {arXiv preprint arXiv:0808.1309},
  year   = {2012}
}

Comments

14 pages, replacement of previous version with more detailed proofs and some corrections

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