English

On a conjecture of H. Gupta

Combinatorics 2010-09-28 v1 Number Theory

Abstract

Denote by r(n) the length of a shortest integer sequence on a circle containing all permutations of the set {1,2,...,n} as subsequences. Hansraj Gupta conjectured in 1981 that r(n) <= n^2/2. In this paper we confirm the conjecture for the case where n is even, and show that r(n) < n^2/2 + n/4 -1 if n is odd.

Keywords

Cite

@article{arxiv.1009.5106,
  title  = {On a conjecture of H. Gupta},
  author = {Emmanuel Lecouturier and David Zmiaikou},
  journal= {arXiv preprint arXiv:1009.5106},
  year   = {2010}
}

Comments

10 pages, 4 figures, 1 table, 7 references