Extended inverse results for restricted h-fold sumset in integers

2025/05/12 by Debyani Manna, Manna, Debyani, Mohan +2
Computer Science · Mathematics · #11970 #11B13 #11B75 #11P70 #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2505.07415

openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a finite set of k integers. For h ≤ k, the restricted h-fold sumset h^\wedge 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^\wedge A when |h^\wedge 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^\wedge A with arbitrary h ≥ 3 and characterize all possible sets A for certain cardinalities of h^\wedge A.

Citations

• Extended inverse theorems for h-fold sumsets in integers
• Some inverse results of sumsets
• A Step Beyond Kemperman's Structure Theorem

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• Direct and Inverse Problems for Restricted Signed Sumsets -- II
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