Ballot numbers, alternating products, and the erdős-heilbronn conjecture

Abstract

Let A be a subset of an abelian group. Let hA denote the set of all sums of h elements of A with repetitions allowed, and let h ∧ A denote the set of all sums of h distinct elements of A, that is, all sums of the form a 1+⋯+a h, where a 1,…, a h ∈A and a i ≠a j for i≠j.