{"paper":{"title":"An Arithmetic Analogue of Fox's Triangle Removal Argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Madhur Tulsiani, Pooya Hatami, Sushant Sachdeva","submitted_at":"2013-04-17T19:11:52Z","abstract_excerpt":"We give an arithmetic version of the recent proof of the triangle removal lemma by Fox [Fox11], for the group $\\mathbb{F}_2^n$.\n  A triangle in $\\mathbb{F}_2^n$ is a triple $(x,y,z)$ such that $x+y+z = 0$. The triangle removal lemma for $\\mathbb{F}_2^n$ states that for every $\\epsilon > 0$ there is a $\\delta > 0$, such that if a subset $A$ of $\\mathbb{F}_2^n$ requires the removal of at least $\\epsilon \\cdot 2^n$ elements to make it triangle-free, then it must contain at least $\\delta \\cdot 2^{2n}$ triangles. This problem was first studied by Green [Gre05] who proved a lower bound on $\\delta$ u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4921","kind":"arxiv","version":3},"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"}