Zero-sum sequences over finite abelian groups and their sets of lengths

Abstract: Let $G$ be an additively written abelian group. A (finite unordered) sequence $S = g_1 \ldots g_{\ell}$ of terms from $G$ (with repetition allowed) is said to be a \emph{zero-sum sequence} if $g_1 + \ldots + g_{\ell} = 0$. Every zero-sum sequence $S$ can be factored into minimal zero-sum sequences, say $S = S_1 \ldots S_k$. Then $k$ is called a factorization length of $S$ and $\mathsf L (S) \subset \mathbb N$ denotes the set of all factorization lengths of $S$. We consider the system $\mathcal L (G) = \big\{ \mathsf L (S) \colon S \ \text{is a zero-sum sequence over $G$} \big\}$ of all sets of lengths.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

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