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Barycentric-sum problems: A survey

Abstract:

Let G be a finite abelian group. A sequence in G is barycentric if it contains one element "average" of its terms. We give a survey of results and open problems concerning sufficient conditions for the existence of barycentric sequences. Moreover values and open problems on the k-barycentric Davenport constant BD(k, G), the barycentric Davenport constant BD(G), the strong k-barycentric Davenport constant SBD(k, G) and barycentric Ramsey numbers BR(H, G) for some graphs H are presented. These constants are related to the Davenport constant D(G).