Journal of Integer Sequences, Vol. 24 (2021), Article 21.4.2

A Note on Sumsets and Restricted Sumsets


Jagannath Bhanja
Harish-Chandra Research Institute
Chhatnag Road, Jhunsi
Prayagraj 211019
India

Abstract:

In this note we find the optimal lower bound for the size of the sumsets HA and $H\,\hat{}A$ over finite sets H, A of nonnegative integers, where $HA = \bigcup_{h\in H} hA$ and $H\,\hat{}A = \bigcup_{h\in H} h\,\hat{}A$. We also find the underlying algebraic structure of the sets A and H for which the size of the sumsets HA and $H\,\hat{}A$ is minimum.

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Received August 22 2020; revised versions received August 23 2020; February 1 2021; March 27 2021; March 28 2021. Published in Journal of Integer Sequences, March 28 2021. Corrigendum posted June 11 2021.

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