Mathematics – Combinatorics
Scientific paper
2010-09-26
Mathematics
Combinatorics
10 pages, 4 figures, 1 table, 7 references
Scientific paper
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.
Lecouturier Emmanuel
Zmiaikou David
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