Additive closedness in subsets of $\mathbb{Z}_n$

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Document Type : Original paper

Authors

1 Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India

2 Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, 576104, India

Abstract

The r-value in subsets of finite abelian groups serves as a metric for evaluating the degree of closedness within these subsets. The notion of the r-value is intricately linked to other mathematical constructs such as sum-free sets, Sidon sets, and Schur triples. We extend the definition of r-value of a subset in a finite abelian group and investigate the r-values of subsets of Z_n, by constructing a formula for r-values of intervals consist of consecutive residue classes modulo n.

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References

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Communications in Combinatorics and Optimization

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Available Online from 20 August 2024

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