{"paper":{"title":"Stanley sequences with odd character","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Richard A. Moy","submitted_at":"2017-07-07T05:04:09Z","abstract_excerpt":"Given a set of integers containing no 3-term arithmetic progressions, one constructs a Stanley sequence by choosing integers greedily without forming such a progression. Independent Stanley sequences are a \"well-structured\" class of Stanley sequences with two main parameters: the character $\\lambda(A)$ and the repeat factor $\\rho(A)$. Rolnick conjectured that for every $\\lambda \\in \\mathbb{N}_0\\backslash\\{1, 3, 5, 9, 11, 15\\}$, there exists an independent Stanley sequence $S(A)$ such that $\\lambda(A) =\\lambda$. This paper demonstrates that $\\lambda(A) \\not\\in \\{1, 3, 5, 9, 11, 15\\}$ for any in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02037","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"}