Inverse zero-sum problems III
By Weidong Gao, Alfred Geroldinger, David J. Grynkiewicz. 2008
62 citations recorded by the source corpus.
Let G be a nite abelian group. The Davenport constant D(G) is the smallest integer ` 2 N such that every sequence S over G of length jSj ` has a nontrivial zero-sum subsequence. Let G = Cn Cn with n 2. Then D(G) = 2n 1, and we say that G has Property B if every minimal zero-sum sequence S over G of length jSj = 2n 1 contains an element with multiplicity n 1. We show that, if m and n are odd and both Cm Cm and Cn Cn have Property B, then Cmn Cmn has Property B. Based on this and various recent and former results by Gao and Geroldinger, by Schmid, and by G. Bhowmik, I. Halupczok and J. C. Schlage-Puchta, the complete characterization of all minimal zero-sum sequences of length D(G) in groups of rank two is reduced to the veri cation of Property B in groups of the form Cp Cp with p prime.
Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/23facbc5917211b55fadc3ffd8e048d4e8f07b3a
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In Discrete Mathematics and Combinatorics
In Electrical and Electronic Engineering
Citations in the corpus
- The Interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics (2015, background): “hows that k= vg(U) >max{vh(U): h∈ G\{g}}, and so gis uniquely determined. The structure of all minimal zero-sum sequences of maximal length D(G) has been completely determined for rank two groups ([26, 28, 69, 61]), for groups of the form G= C 2 ⊕C 2 ⊕C 2nwith n≥ 2 ([70, Theorem 3.13]), and for g”
- Inverse zero-sum problems II (2008, background): “By a very recent result (see [11], and [9] for an earlier partial result) it is known that to establish Property B for C2 m for each m ∈ N, it suffices to establish it for C2 p for each prime p.”