Some inverse results of sumsets

2019/11/03 by Min Tang, Yun Xing, Tang, Min +1 · 2 citations
Computer Science · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1911.00854

openalex publication_date 2019/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let h≥ 2 and A=\a₀,a₁,…,a_k-1\ be a finite set of integers. It is well-known that |hA|=hk-h+1 if and only if A is a k-term arithmetic progression. In this paper, we give some nontrivial inverse results of the sets A with some extrema the cardinalities of hA.

Cited by

• On the Sumset of Sets of Size k
• Extended inverse results for restricted h-fold sumset in integers

Related

• Extended inverse theorems for h-fold sumsets in integers
• On the structure of the h-fold sumsets
• On an inverse problem in additive number theory
• k-term Arithmetic Progressions in Sumsets
• Extended inverse results for restricted h-fold sumset in integers