Abstract
Let G be a finite additive abelian group with exponent \(d^kn, d,n>1,\) and k a positive integer. For a sequence S over G and \(A=\{1,2,\ldots ,d^kn-1\}\setminus \{d^kn/d^i:i\in [1,k]\}, \) we investigate the lower bound of the number \(N_{A,0}(S)\), which denotes the number of A-weighted zero-sum subsequences of S. In particular, we prove that \(N_{A,0}(S)\ge 2^{|S|-D_A(G)+1},\) where \(D_A(G)\) is the A-weighted Davenport Constant. We also characterize the structures of the extremal sequences for which equality holds for some groups.
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The authors would like to express their gratitude to the referees for their helpful suggestions which improved the presentation of this paper.
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The authors were partially supported by FAPEMIG grant RED-00133-21 and by FAPEMIG grant APQ-02546-21.
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A. T. Silva have partially supported by FAPEMIG APQ-02546-21 and RED-00133-21.
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Lemos, A., Moriya, B.K., Moura, A.O. et al. On the number of weighted zero-sum subsequences. Period Math Hung 87, 366–373 (2023). https://doi.org/10.1007/s10998-023-00533-6
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DOI: https://doi.org/10.1007/s10998-023-00533-6