B_h-sets and perturbations in normed vector spaces

Abstract: The subset $A = \{a_i:i \in I\}$ of a normed vector space is a $B_h$-set if every element of the sumset $hA$ has a unique representation as a sum of $h$ elements of $A$. An $\varepsilon$-perturbation of $A$ is a set $A' = \{a'_i:i\in I\}$ such that $|a'-a|<\varepsilon$ for all $i \in I$. Let $\Delta_{hA} = \inf\{|x'-x| : x,x' \in hA \text{ and } x\neq x'\}$. It is proved that if $A$ is finite or countably infinite set with $\Delta_{hA}>0$, then there is a $B_h$-set $A'$ that is an $\varepsilon$-perturbation of $A$.

commutative algebracombinatoricsnumber theory

Audience: researchers in the topic

New York Number Theory Seminar

Series comments: Meeting ID: 840 6618 4717 Passcode: 304403