A note on sumsets and difference sets in groups of order 12

Neetu; Anupriya  Shetty; B R Shankar

doi:10.5269/bspm.78446

Neetu National Institute of Technology Karnataka, Surathkal
Anupriya Shetty Department of Mathematics, St Aloysius (Deemed to be University), Mangaluru, Karnataka, 575003, India
B R Shankar National Institute of Technology Karnataka, Surathkal

Abstract

A subset $A$ of a group $G$ is referred to as a balanced set when $|A+A|=|A-A|$, MSTD (more sums than differences) when $|A+A|>|A-A|$, and MDTS (more differences than sums) when $|A-A|>|A+A|$. In this paper, we present a comparative study of MSTD and MDTS sets in groups of order 12 up to isomorphism. Additionally, we have completely categorized such sets in these groups and have provided a set $A$ with the current highest value of $ln(|A+A|)/ln(|A-A|).$

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