Some remarks on barycentric-sum problems over cyclic groups

We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer l such that each subset A of G with at least l elements contains a subset with k elements {g_1, ..., g_k} satisfying g_1 + ... + g_k = k g_j for some 1 <= j <= k.Comment: to appear in European Journal of Combinatoric

Some remarks on barycentric-sum problems over cyclic groups

Abstract. We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer ℓ such that each subset A of G with at least ℓ elements contains a subset with k elements {g1,...,gk} satisfying g1 +···+gk = k gj for some 1 ≤ j ≤ k. hal-00689464, version 2- 19 Jun 2013 1