Three problems in additive number theory

Abstract: This will be an introduction to three (possibly new) problems in additive number theory. The first concerns the range and frequencies of the sizes of sumsets of finite sets of integers. The second considers the sets $H$ of integers such that there exists an increasing sequence $(A_i)_{i=1}^{\infty} A_i$ of sets of integers such that $h \in H$ if and only if $h\bigcap_{i=1}^{\infty} A_i = \bigcap_{i=1}^{\infty} hA_i$. The third asks about the possible sizes of $h$-bases for $n$ for finite sets of integers that contain at least one negative integer.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory seminar (CANT 2026)