{"paper":{"title":"Asymptotic enumeration of sparse uniform linear hypergraphs with given degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine Greenhill, Vladimir Blinovsky","submitted_at":"2014-09-04T03:42:48Z","abstract_excerpt":"A hypergraph is simple if it has no loops and no repeated edges, and a hypergraph is linear if it is simple and each pair of edges intersects in at most one vertex. For $n\\geq 3$, let $r= r(n)\\geq 3$ be an integer and let $\\boldsymbol{k} = (k_1,\\ldots, k_n)$ be a vector of nonnegative integers, where each $k_j = k_j(n)$ may depend on $n$. Let $M = M(n) = \\sum_{j=1}^n k_j$ for all $n\\geq 3$, and define the set $\\mathcal{I} = \\{ n\\geq 3 \\mid r(n) \\text{ divides } M(n)\\}$. We assume that $\\mathcal{I}$ is infinite, and perform asymptotics as $n$ tends to infinity along $\\mathcal{I}$. Our main resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1314","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"}