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arXiv · 2404.11312

A note on weighted consecutive Davenport constant

A. Lemos·A. O. Moura·S. Ribas·A. T. Silva
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Abstract

Let $G$ be a group and $A\subseteq [1,\exp(G)-1]$. We define the constant ${\sf C}_A(G),$ which is the least positive integer $\ell$ such that every sequence over $G$ of length at least $\ell$ has an $A$-weighted consecutive product-one subsequence. In this paper, among other things, we prove that ${\sf C}_A(C_n^2)=4$ with $A=[1,n-1],$ and ${\sf C}(H\times K)=|H||K|$, where $H$ is a finite abelian group and $K$ is a metacyclic group.

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A. Lemos, A. O. Moura, S. Ribas, A. T. Silva. 2024-04-17. A note on weighted consecutive Davenport constant. https://arxiv.org/abs/2404.11312

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