Extended Inverse results for restricted h-fold sumset in integer

Abstract: Let $A$ be a finite set of $k$ integers. For $2 \leq h \leq k$, the restricted h-fold sumset $h^{\wedge}A$ is the set of all sums of $h$ distinct elements of the set $A$. 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 $h^{\wedge}A$ when $|h^{\wedge}A|$ is small. For $h \in \{2,3,4\}$, this question has already been studied by Mohan and Pandey. In this article, we study the inverse problems for $h^{\wedge}A$ with arbitrary $h \geq 3$ and characterize all possible sets $A$ for certain cardinalities of $h^{\wedge}A$. Joint work with Mohan and Ram Krishna Pandey.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory seminar (CANT 2026)