A note on iterated sumsets races

2025/05/16 by Paul Péringuey, Péringuey, Paul, Anne de Roton +1 · 1 citation
Computer Science · Mathematics · #11P70 #Analytic Number Theory Research #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.11233

openalex publication_date 2025/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This short note answers a question raised by Nathanson \citeNath25 about "races" between iterated sumsets. We prove that for any integer n, there are finite sets of integers A and B with same diameter such that the signs of the elements of the sequence (|hA|-|hB|)_h changes at least n times. Kravitz proved in \citeKravitz a much better result. This brief and modest note may serve as a stepping stone towards his work.

Citations

• Finer control on relative sizes of iterated sumsets
• Relative sizes of iterated sumsets
• INTERSECTIONS OF SUMSETS IN ADDITIVE NUMBER THEORY
• Problems in additive number theory, VI: Sizes of sumsets

Cited by

• Triangular and tetrahedral number differences of sumset sizes in additive number theory
• Explicit sumset sizes in additive number theory

Related

• Finer control on relative sizes of iterated sumsets
• Consecutive integers in high-multiplicity sumsets
• A result on the size of iterated sumsets in ℤ^d
• Additive sumset sizes with tetrahedral differences
• Triangular gaps in the most frequent sizes of hA for |A|=4