All sums of distinct terms of a sequence

For A ⊆ Z , we study the gaps in the sequence of all sums of h pairwise distinct elements of A . For example, the following result is proved: for any integer h ≥ 3 , there exists A ⊆ Z such that every integer can be uniquely (neglecting the order) represented as a sum of h not necessarily distinct elements of A , and for any integer ℓ ≥ 1 , in the sequence of all sums of ℓ pairwise distinct elements of A , the gaps can be arbitrarily large. Several questions are posed in this paper.