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