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 {g_1, ... , g_k} satisfying g_1 + ... + g_k = k g_j for some 1 <= j <= k.
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Oscar Ordaz, Alain Plagne, Wolfgang A. Schmid. Some remarks on barycentric-sum problems over cyclic groups. European Journal of Combinatorics, Elsevier, 2013, 34 (8), pp.1415-1428. ⟨10.1016/j.ejc.2013.05.025⟩. ⟨hal-00689464v2⟩

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