{"paper":{"title":"Negligible obstructions and Tur\\'an exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma, Tao Jiang, Zilin Jiang","submitted_at":"2020-07-06T18:02:37Z","abstract_excerpt":"We show that for every rational number $r \\in (1,2)$ of the form $2 - a/b$, where $a, b \\in \\mathbb{N}^+$ satisfy $\\lfloor b/a \\rfloor^3 \\le a \\le b / (\\lfloor b/a \\rfloor +1) + 1$, there exists a graph $F_r$ such that the Tur\\'an number $\\operatorname{ex}(n, F_r) = \\Theta(n^r)$. Our result in particular generates infinitely many new Tur\\'an exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh--Conlon conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.02975","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.02975/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}