{"paper":{"title":"Sets of large dimension not containing polynomial configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andr\\'as M\\'ath\\'e","submitted_at":"2012-01-02T22:41:26Z","abstract_excerpt":"The main result of this paper is the following. Given countably many multivariate polynomials with rational coefficients and maximum degree $d$, we construct a compact set $E\\subset \\R^n$ of Hausdorff dimension $n/d$ which does not contain finite point configurations corresponding to the zero sets of the given polynomials.\n  Given a set $E\\subset \\R^n$, we study the angles determined by three points of $E$. The main result implies the existence of a compact set in $\\R^n$ of Hausdorff dimension $n/2$ which does not contain the angle $\\pi/2$. (This is known to be sharp if $n$ is even.) We show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0548","kind":"arxiv","version":1},"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"}