Some remarks on barycentric-sum problems over cyclic groups

Oscar Ordaz (1) , Alain Plagne (2) , Wolfgang A. Schmid (3)

1 Laboratorio MoST, Centro ISYS
2 CMLS - Centre de Mathématiques Laurent Schwartz
3 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: barycentric sum; zero-sum problem; finite abelian group

Domaines: Théorie des nombres [math.NT]; Combinatoire [math.CO]

Oscar Ordaz, Alain Plagne, Wolfgang A. Schmid. Some remarks on barycentric-sum problems over cyclic groups. European Journal of Combinatorics, 2013, 34 (8), pp.1415-1428. ⟨10.1016/j.ejc.2013.05.025⟩. ⟨hal-00689464v2⟩