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- W4302569612 abstract "Let $mathcal S$ be a multiset of integers. We say $mathcal S$ is a $textit{zero-sum sequence}$ if the sum of its elements is 0. We study zero-sum sequences whose elements lie in the interval $[-k,k]$ such that no subsequence of length $t$ is also zero-sum. Given these restrictions, Augspurger, Minter, Shoukry, Sissokho, Voss show that there are arbitrarily long $t$-avoiding, $k$-bounded zero-sum sequences unless $t$ is divisible by $mathrm{LCM}(2,3,4,dots,2k-1)$. We confirm a conjecture of these authors that for $k$ and $t$ such that this divisibility condition holds, every zero-sum sequence of length at least $t+k^2-k$ contains a zero-sum subsequence of length $t$, and that this is the minimal length for which this property holds." @default.
- W4302569612 created "2022-10-06" @default.
- W4302569612 creator A5061144291 @default.
- W4302569612 date "2016-08-14" @default.
- W4302569612 modified "2023-09-27" @default.
- W4302569612 title "An Analogue of the ErdH{o}s-Ginzburg-Ziv Theorem over $mathbb Z$" @default.
- W4302569612 doi "https://doi.org/10.48550/arxiv.1608.04125" @default.
- W4302569612 hasPublicationYear "2016" @default.
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