On a conjecture of H. Gupta

Denote by r(n)r(n) the length of a shortest integer sequence on a circle containing all permutations of the set {1,2,…,n}{1,2,…,n} as subsequences. Hansraj Gupta conjectured in 19811981 that r(n)⩽n22. In this paper, we confirm the conjecture for the case where nn is even and show that r(n)