INTERSECTIONS OF SUMSETS IN ADDITIVE NUMBER THEORY

2024/12/20 by Melvyn B. Nathanson, Nathanson, Melvyn B. · 3 citations
Decision Sciences · Mathematics · #Fuzzy and Soft Set Theory #Functional Equations Stability Results #Fixed Point Theorems Analysis

paper · pdf · doi:10.1017/s0004972726101270

Abstract

Abstract Let A be a subset of an additive abelian semigroup S and let hA be the h -fold sumset of A . The following question is considered. Let (A_q)_q=1^∞ be a strictly decreasing sequence of sets in S and let A = \bigcap _q=1^∞ A_q . When does one have \beginalign* hA = \bigcap_q=1^∞ hA_q \endalign* for some or all h ≥ 2 ?

Citations

• Possible Sizes of Sumsets
• Compression and complexity for sumset sizes in additive number theory

Cited by

• Compression and complexity for sumset sizes in additive number theory
• Diversity, equity, and inclusion for problems in additive number theory
• Additive sumset sizes with tetrahedral differences

Related

• A problem on sumset sizes of sets of lattice points
• On the Sumset of Sets of Size k
• Explicit sumset sizes in additive number theory
• Problems in additive number theory, VI: Sizes of sumsets
• Sumsets with a minimum number of distinct terms