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Constrained and generalized barycentric Davenport constants

Abstract:

Let G be a finite abelian group. The constrained barycentric Davenport constant BDs(G) with s ≥ 2, is the smallest positive integer d such that every sequence with d terms in G contains a k-barycentric subsequence with 2 ≤ k ≤ s. The generalized barycentric Davenport constant BD s(G), s ≥ 1, is the least positive integer d such that in every sequence with d terms there exist s disjoint barycentric subsequences. For s = 1, this is just the barycentric Davenport constant BD(G). Relations among BDs(G), BDs(G) and BD(G) are established, these constants are related to the Davenport constant D(G). Some values or bounds of BD s(G), BDs(G) and BD(G) are given.