{"paper":{"title":"Rainbow arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Erickson, Derrick Stolee, Jephian Chin-Hung Lin, Kirsten Hogenson, Leslie Hogben, Lucas Kramer, Michael Young, Nathan Warnberg, Richard L. Kramer, Ryan R. Martin, Steve Butler","submitted_at":"2014-04-29T04:24:57Z","abstract_excerpt":"In this paper, we investigate the anti-Ramsey (more precisely, anti-van der Waerden) properties of arithmetic progressions. For positive integers $n$ and $k$, the expression $aw([n],k)$ denotes the smallest number of colors with which the integers $\\{1,\\ldots,n\\}$ can be colored and still guarantee there is a rainbow arithmetic progression of length $k$. We establish that $aw([n],3)=\\Theta(\\log n)$ and $aw([n],k)=n^{1-o(1)}$ for $k\\geq 4$.\n  For positive integers $n$ and $k$, the expression $aw(Z_n,k)$ denotes the smallest number of colors with which elements of the cyclic group of order $n$ c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7232","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"}