{"paper":{"title":"Erd\\H{o}s-Ginzburg-Ziv constants by avoiding three-term arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Jacob Fox, Lisa Sauermann","submitted_at":"2017-08-30T03:53:29Z","abstract_excerpt":"For a finite abelian group $G$, the Erd\\H{o}s-Ginzburg-Ziv constant $\\mathfrak{s}(G)$ is the smallest $s$ such that every sequence of $s$ (not necessarily distinct) elements of $G$ has a zero-sum subsequence of length $\\operatorname{exp}(G)$. For a prime $p$, let $r(\\mathbb{F}_p^n)$ denote the size of the largest subset of $\\mathbb{F}_p^n$ without a three-term arithmetic progression. Although similar methods have been used to study $\\mathfrak{s}(G)$ and $r(\\mathbb{F}_p^n)$, no direct connection between these quantities has previously been established. We give an upper bound for $\\mathfrak{s}(G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09100","kind":"arxiv","version":2},"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"}