Abstract
Let G be an additive abelian group and h be a positive integer. For a nonempty finite subset A={a0,a1,…,ak−1} of G, we leth+_A:={Σi=0k−1λiai:(λ0,…,λk−1)∈Zk,Σi=0k−1|λi|=h}, be the h-fold signed sumset of A.The direct problem for the signed sumset h+_A is to find a nontrivial lower bound for |h+_A| in terms of |A|. The inverse problem for h+_A is to determine the structure of the finite set A for which |h+_A| is minimal. In this article, we solve both the direct and inverse problems for |h+_A|, when A is a finite set of integers.
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