Restricted-sum-dominant sets

Abstract

Let $A$ be a nonempty finite subset of an additive abelian group $G$. Define $A+A:=\{a+b:a,b\in A\}$ and $A\dotplus A:=\{a+b:a,b\in A\text{and}a\ne b\}$. The set $A$ is called a {\em sum-dominant (SD) set} if $|A+A|>|A-A|$, and it is called a {\em restricted sum-domonant (RSD) set} if $|A\dotplus A|>|A-A|$. In this paper, we prove that for infinitely many positive integers $k$, there are infinitely many RSD sets of integers of cardinality $k$. We also provide an explicit construction of infinite sequence of RSD sets.

7 pages