Intersections of 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 $(A_q{)}_{q=1}^{\infty }$ be a strictly decreasing sequence of sets in $S$ and let $A={\bigcap }_{q=1}^{\infty }{A}_q$. When does one have \[ hA = \bigcap_{q=1}^{\infty} hA_q \] for some or all $h\ge 2$?

Corrected and expanded with new results added; 8 pages

References in corpus (2)

• Compression and complexity for sumset sizes in additive number theory
• Explicit sumset sizes in additive number theory