Extremal sequences for a weighted zero-sum constant

Abstract

The constant $C_A(n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in ${\mathbb{Z}}_n$ has a subsequence of consecutive terms whose $A$-weighted sum is zero, where the weight set $A\subseteq {\mathbb{Z}}_n\setminus \{0\}$. If $C_A(n)=k$, then a sequence in ${\mathbb{Z}}_n$ of length $k-1$ which has no $A$-weighted zero-sum subsequence of consecutive terms is called an $A$-extremal sequence. We characterize these sequences for some particular weight sets.

arXiv comment18 pages. arXiv admin note: substantial text overlap with arXiv:2110.02539