On the Number of Weighted Zero-sum Subsequences

2022/09/29 by Anderson Alves de Araújo de Lemos, B. K. Moriya, Lemos, A. +5
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2209.14779

openalex publication_date 2022/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite additive abelian group with exponent d^kn, d,n>1, and k a positive integer. For S a sequence over G and A=\1,2,…,d^kn-1\∖\d^kn/dⁱ:i∈[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)≥ 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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