On a conjecture of H. Gupta
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) <= n2/2. In this paper we confirm the conjecture for the case where n is even, and show that r(n) < n2/2 + n/4 -1 if n is odd.
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