April 17, 2024Open Access

A note on weighted consecutive Davenport constant

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Abstract

Let G be a group and A 1, (G) -1. We define the constant CA (G), which is the least positive integer such that every sequence over G of length at least has an A-weighted consecutive product-one subsequence. In this paper, among other things, we prove that CA (Cₙ²) =4 with A=1, n-1, and C (H K) =|H||K|, where H is a finite abelian group and K is a metacyclic group.

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Lemos et al. (Wed,) studied this question.

synapsesocial.com/papers/68e6ecccb6db643587667db7 https://doi.org/https://doi.org/10.48550/arxiv.2404.11312

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5On zero-sum subsequences in a finite abelian group of length not exceeding a given number2025

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