Remarks on a generalization of the Davenport constant

A generalization of the Davenport constant is investigated. For a finite abelian group G and a positive integer k, let Dk(G) denote the smallest such that each sequence over G of length at least has k disjoint non-empty zero-sum subsequences. For general G, expanding on known results, upper and lower bounds on these invariants are investigated and it is proved that the sequence (Dk(G))kN is eventually an arithmetic progression with difference exp(G), and several questions arising from this fact are investigated. For elementary 2-groups, Dk(G) is investigated in detail; in particular, the exact values are determined for groups of rank four and five (for rank at most three they were already known).

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Michael Freeze, Wolfgang A. Schmid
• Keywords: DM 2010, Finite Abelian Group, Non-empty Zero-sum Subsequences, Positive Integer