Some results on the extended inverse problem of $A+2 \cdot A$

Abstract: Let $A$ be a finite set of integers and $A+ 2 \cdot A= \{a+2a': a,a' \in A\}$. An extended inverse problem associated with the sumset $A+2 \cdot A$ is to determine the underlying set $A$ when the size of the sumset $A+2 \cdot A$ deviates from the minimum possible size. We find all possible arithmetic structures of $A$ for certain cardinalities of $A + 2 \cdot A$ and use them to address extended inverse problems in the Baumslag-Solitar group $BS(1,2)$. This is joint work with Ram Krishna Pandey.

Mathematics

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2025)