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arXiv · 2111.01018

Extremal sequences for a weighted zero-sum constant

Santanu Mondal·Krishnendu Paul·Shameek Paul
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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.

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Santanu Mondal, Krishnendu Paul, Shameek Paul. 2021-11-01. Extremal sequences for a weighted zero-sum constant. https://arxiv.org/abs/2111.01018

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