On a conjecture of H. Gupta

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.