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arXiv · 1712.09226

Restricted-sum-dominant sets

Raj Kumar Mistri·R. Thangadurai
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Abstract

Let $A$ be a nonempty finite subset of an additive abelian group $G$. Define $A + A := \{a + b : a, b \in A\}$ and $A \dotplus A := \{a + b : a, b \in A~\text{and}~ a \neq b\}$. 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.

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Raj Kumar Mistri, R. Thangadurai. 2017-12-26. Restricted-sum-dominant sets. https://arxiv.org/abs/1712.09226

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