Long Zero-Sum Free Sequences over Cyclic Groups

Abstract

From previous chapters, we know that a zero-sum free sequence Open image in new window 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.