{"paper":{"title":"On polynomial configurations in fractal sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Izabella Laba, Kevin Henriot, Malabika Pramanik","submitted_at":"2015-11-18T16:55:03Z","abstract_excerpt":"We show that subsets of $\\mathbb{R}^n$ of large enough Hausdorff and Fourier dimension contain polynomial patterns of the form \\begin{align*}\n  ( x ,\\, x + A_1 y ,\\, \\dots,\\, x + A_{k-1} y ,\\, x + A_k y + Q(y) e_n ),\n  \\quad x \\in \\mathbb{R}^n,\\ y \\in \\mathbb{R}^m, \\end{align*} where $A_i$ are real $n \\times m$ matrices, $Q$ is a real polynomial in $m$ variables and $e_n = (0,\\dots,0,1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05874","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"}