Weighted Sequences in Finite Cyclic Groups

2007/10/19 by David J. Grynkiewicz, Grynkiewicz, David J., Jujuan Zhuang +1 · 1 citation
Mathematics · #11B75: 11B50 #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0710.3718

openalex publication_date 2007/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p>7 be a prime, let G=\Z/p\Z, and let S₁=∏_i=1^p g_i and S₂=∏_i=1^p h_i be two sequences with terms from G. Suppose that the maximum multiplicity of a term from either S₁ or S₂ is at most (2p+1)/(5). Then we show that, for each g∈ G, there exists a permutation σ of 1,2,..., p such that g=∑_i=1^p(g_i⋅ h_σ(i)). The question is related to a conjecture of A. Bialostocki concerning weighted subsequence sums and the Erdős-Ginzburg-Ziv Theorem.

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• A Weighted Generalization of Two Theorems of Gao

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