On a partition analog of the cauchy-davenport theorem


Let G be a finite abelian group, and let n be a positive integer. From the Cauchy-Davenport Theorem it follows that if G is a cyclic group of prime order, then any collection of n subsets A1, A2,..., An of G satisfies ∑ M. Kneser generalized the Cauchy-Davenport Theorem for any abelian group. In this paper, we prove a sequence-partition analog of the Cauchy-Davenport Theorem along the lines of Kneser's Theorem. A particular case of our theorem was proved by J. E. Olson in the context of the Erdos-Ginzburg-Ziv Theorem. © 2005 Akadémiai Kiadó, Budapest.

Publication Title

Acta Mathematica Hungarica