Resumo

MARCHAN, Luz; ORDAZ, Oscar; SALAZAR, José  e  VILLARROEL, Felicia. Existence conditions for k-barycentric olson constant. Rev. Mat [online]. 2021, vol.28, n.1, pp.39-53. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v28i1.33773.

Let (G, +) be a finite abelian group and 3 ≤ k ≤ |G| a positive integer. The k-barycentric Olson constant denoted by BO(k, G) is defined as the smallest integer ℓ such that each set A of G with |A| = ℓ contains a subset with k elements {a1, . . . , ak} satisfying a1 + · · · + ak = kaj for some 1 ≤ j ≤ k. We establish some general conditions on G assuring the existence of BO(k, G) for each 3 ≤ k ≤ |G|. In particular, from our results we can derive the existence conditions for cyclic groups and for elementary p-groups p ≥ 3. We give a special treatment over the existence condition for the elementary 2-groups.

Palavras-chave : finite abelian group; zero-sum problem; baricentric-sum problem; Davenport constant; k-barycentric Olson constant..

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