A reciprocity on finite abelian groups involving zero-sum sequences II

2022/01/30 by Maosheng Li, Li, Mao-Sheng, Hanbin Zhang +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2201.12821

openalex publication_date 2022/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite abelian group. For any positive integers d and m, let φ_G(d) be the number of elements in G of order d and \mathsf M(G,m) be the set of all zero-sum sequences of length m. In this paper, for any finite abelian group H, we prove that |\mathsf M(G,|H|)|=|\mathsf M(H,|G|)| if and only if φ_G(d)=φ_H(d) for any d|(|G|,|H|). We also consider an extension of this result to non-abelian groups in terms of invariant theory.

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