Note on the index conjecture in zero-sum theory and its connection to a Dedekind-type sum

2016/06/06 by Fan Ge, Ge, Fan · 1 citation
Mathematics · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1606.01605

Abstract

Let S=(a₁)⋯(a_k) be a minimal zero-sum sequence over a finite cyclic group G. The index conjecture states that if k=4 and gcd(|G|,6)=1, then S has index 1. In this note we study the index conjecture and connect it to a Dedekind-type sum. In particular we reprove a special case of the conjecture when |G| is prime.

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• Improved Bounds for the Index Conjecture in Zero-Sum Theory

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