On the Structure of Minimal Zero-Sum Sequences With Maximal Cross Number (pp. 109-126)
Authors: Alfred Geroldinger and David J. Grynkiewicz
Abstract: Let G be an additive finite abelian group, S = g1 • . . . • gl a sequence over G and k(S) = ord(g1)-1 +. . .+ord(gl)-1 its cross number. Then the cross number K(G) of G is defined as the maximal cross number of all minimal zero-sum sequences over G. In the spirit of inverse additive number theory, we study the structure of those minimal zero-sum sequences S over G whose cross number equals K(G). These questions are motivated by applications in the theory of non-unique factorizations.