Let A be a finite set of k integers. For h k, the restricted h-fold sumset h^ A is the set of all sums of h distinct elements of A. In additive combinatorics, much of the focus has traditionally been on finite integer sets whose sumsets are unusually small (cf. \ Freiman's theorem and its extensions). More recently, Nathanson posed the inverse problem for the restricted sumset h^ A when |h^ A| is small. For h \2, 3, 4\, this question has already been studied by Mohan and Pandey. In this article, we study the inverse problems for h^ A with arbitrary h 3 and characterize all possible sets A for certain cardinalities of h^ A.
Manna et al. (Mon,) studied this question.