Sumsets of zerofree sequences

Abstract EN

Let G be a finite abelian group.

A sequence P = {£,,..., g,) of elements of G, possibly with repetitions, is zerofree if no subsequence of P sums to zero.

We consider the set of sums of subsequences of P and establish bounds on the cardinality of this set determined by the length and cardinality of the sequence.

We discuss the structure of P in the critical case where the bound is obtained.

We also study the growth of these sumsets when additional elements are appended to P.

In the context of these sets, an interesting generalization of Vosper’s Theorem from additive number theory is obtained.