{"paper":{"title":"An Analogue of the Erd\\H{o}s-Ginzburg-Ziv Theorem over $\\mathbb Z$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Aaron Berger","submitted_at":"2016-08-14T19:13:06Z","abstract_excerpt":"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 seque"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04125","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}