{"paper":{"title":"Avoiding zero-sum subsequences of prescribed length over the integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Augspurger, K. Shoukry, K. Voss, M. Minter, P. Sissokho","submitted_at":"2016-03-13T01:02:31Z","abstract_excerpt":"Let $t$ and $k$ be a positive integers, and let $I_k=\\{i\\in \\mathbb{Z}:\\; -k\\leq i\\leq k\\}$. Let $\\mathsf{s}'_t(I_k)$ be the smallest positive integer $\\ell$ such that every zero-sum sequence $S$ over $I_k$ of length $|S|\\ge \\ell$ contains a zero-sum subsequence of length $t$. If no such $\\ell$ exists, then let $\\mathsf{s}'_t(I_k)=\\infty$.\n  In this paper, we prove that $\\mathsf{s}'_t(I_k)$ is finite if and only if every integer in $[1,D(I_k)]$ divides $t$, where $D(I_k)=\\max\\{2,2k-1\\}$ is the Davenport constant of $I_k$. Moreover, we prove that if $\\mathsf{s}'_t(I_k)$ is finite, then $t+k(k-1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03978","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"}