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Long Zero-Sum Free Sequences over Cyclic Groups

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Structural Additive Theory

Part of the book series: Developments in Mathematics ((DEVM,volume 30))

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Abstract

From previous chapters, we know that a zero-sum free sequence has length at most D(C n )−1=n−1. The goal of this chapter is characterize the structure of those zero-sum free sequences close to the extremal possible length. In fact, we will be able to characterize this structure for sequences quite a ways away from the maximal value, namely, for sequences of length roughly half the maximal possible length. This stands in stark contrast to what is known for extremal zero-sum free sequence over more general finite abelian groups: In general, the value D(G) is not known apart from several families of groups, and even in the simplest noncyclic case for which the value of D(G) is known—rank 2 groups—it is only very recently, and with a massive amount of effort, that the structure of sequences simply attaining the equality D(C m ⊕C n )−1 has been determined.

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  1. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Graz, Austria

    David J. Grynkiewicz

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  1. David J. Grynkiewicz
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Grynkiewicz, D.J. (2013). Long Zero-Sum Free Sequences over Cyclic Groups. In: Structural Additive Theory. Developments in Mathematics, vol 30. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00416-7_11

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