What question did this study set out to answer?

The aim is to determine when the h-fold sumset of an intersection of sets equals the intersection of their h-fold sumsets.

May 16, 2026Bulletin of the Australian Mathematical SocietyOpen Access

Intersections of Sumsets in Additive Number Theory

View Full Paper

Ask AI

Bookmark

The aim is to determine when the h-fold sumset of an intersection of sets equals the intersection of their h-fold sumsets.
Defined a sequence of sets in an additive abelian semigroup
Analyzed conditions for equality using mathematical set theory
Delineated specific conditions under which $$ hA = \bigcap_{q=1}^{\infty} hA_q $$ holds for $h \geq 2$
Identified characteristics of the sequence $(A_q)$ needed for the equality to occur

Implication

Investigates the conditions for equality between intersecting h-fold sumsets in additive number theory.

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 (Aq)q=1∞ be a strictly decreasing sequence of sets in S and let A = q=1∞ Aq . When does one have align* hA = q=1∞ hAq align* for some or all h ≥ 2 ?

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Melvyn B. Nathanson (2026) studied this question.

synapsesocial.com/papers/6a080af2a487c87a6a40d052 https://doi.org/10.1017/s0004972726101270

View Full Paper

Ask AI

Bookmark

Implication

Investigates the conditions for equality between intersecting h-fold sumsets in additive number theory.

Intersections of Sumsets in Additive Number Theory

Key Points

Implication

Abstract

Discussion

Cite This Study

Intersections of Sumsets in Additive Number Theory

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading