{"paper":{"title":"Enumerating sparse uniform hypergraphs with given degree sequence and forbidden edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine Greenhill, Haya S. Aldosari","submitted_at":"2018-05-14T02:47:51Z","abstract_excerpt":"For $n\\geq 3$ and $r=r(n) \\geq 3$, let $\\boldsymbol{k} =\\boldsymbol{k}(n)=(k_1, \\ldots, k_n)$ be a sequence of non-negative integers with sum $M(\\boldsymbol{k})=\\sum_{j=1}^{n} k_j$. We assume that $M(\\boldsymbol{k})$ is divisible by $r$ for infinitely many values of $n$, and restrict our attention to these values. Let $X=X(n)$ be a simple $r$-uniform hypergraph on the vertex set $V=\\{v_1,v_2, \\ldots, v_n\\}$ with $t$ edges and maximum degree $x_{\\max}$. We denote by $\\mathcal{H}_r(\\boldsymbol{k})$ the set of all simple $r$-uniform hypergraphs on the vertex set $V$ with degree sequence $\\boldsym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04991","kind":"arxiv","version":4},"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"}