{"paper":{"title":"The van der Waerden complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Likith Govindaiah, Margaret Readdy, Peter S. Park, Richard Ehrenborg","submitted_at":"2016-05-02T20:03:12Z","abstract_excerpt":"We introduce the van der Waerden complex ${\\rm vdW}(n,k)$ defined as the simplicial complex whose facets correspond to arithmetic progressions of length $k$ in the vertex set $\\{1, 2, \\ldots, n\\}$. We show the van der Waerden complex ${\\rm vdW}(n,k)$ is homotopy equivalent to a $CW$-complex whose cells asymptotically have dimension at most $\\log k / \\log \\log k$. Furthermore, we give bounds on $n$ and $k$ which imply that the van der Waerden complex is contractible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00663","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"}