{"paper":{"title":"On the algebraic and topological structure of the set of Tur\\'an densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Codrut Grosu","submitted_at":"2014-03-19T00:25:54Z","abstract_excerpt":"The present paper is concerned with the various algebraic structures supported by the set of Tur\\'an densities.\n  We prove that the set of Tur\\'an densities of finite families of r-graphs is a non-trivial commutative semigroup, and as a consequence we construct explicit irrational densities for any r >= 3. The proof relies on a technique recently developed by Pikhurko.\n  We also show that the set of all Tur\\'an densities forms a graded ring, and from this we obtain a short proof of a theorem of Peng on jumps of hypergraphs.\n  Finally, we prove that the set of Tur\\'an densities of families of r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4653","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"}