Abstract
Let G be a finite abelian group of exponent n and let A be a non-empty subset of \([1,n-1]\). The Davenport constant of G with weight A, denoted by \(D_A(G)\), is defined to be the least positive integer \(\ell \) such that any sequence over G of length \(\ell \) has a non-empty A-weighted zero-sum subsequence. Similarly, the combinatorial invariant \(E_{A}(G)\) is defined to be the least positive integer \(\ell \) such that any sequence over G of length \(\ell \) has an A-weighted zero-sum subsequence of length |G|. In this article, we consider the problem of determining an upper bound of the constants \(E_A({\mathbb {Z}}/n{\mathbb {Z}})\) and \(D_A({\mathbb {Z}}/n{\mathbb {Z}})\), where A is the set of all cubes in \(({\mathbb {Z}}/n{\mathbb {Z}})^*\).
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Acknowledgements
The author would like to sincerely thank Prof. R. Thangadurai and Prof. S. D. Adhikari for going through the paper very carefully. He thanks the referee for going through the manuscript meticulously and giving suggestions to improve the presentation of the paper. He is also grateful to the Department of Atomic Energy, Government of India and Harish-Chandra Research Institute for providing financial support to carry out this research.
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Sarkar, S. Generalization of some weighted zero-sum theorems. Proc Math Sci 131, 32 (2021). https://doi.org/10.1007/s12044-021-00631-w
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DOI: https://doi.org/10.1007/s12044-021-00631-w