{"paper":{"title":"Counting and packing Hamilton $\\ell$-cycles in dense hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asaf Ferber, Benny Sudakov, Michael Krivelevich","submitted_at":"2014-06-12T00:49:54Z","abstract_excerpt":"We consider problems about packing and counting Hamilton $\\ell$-cycles in hypergraphs of large minimum degree. Given a hypergraph $\\mathcal H$, for a $d$-subset $A\\subseteq V(\\mathcal H)$, we denote by $d_{\\mathcal H}(A)$ the number of distinct \\emph{edges} $f\\in E(\\mathcal H)$ for which $A\\subseteq f$, and set $\\delta_d(\\mathcal H)$ to be the minimum $d_{\\mathcal H}(A)$ over all $A\\subseteq V(\\mathcal H)$ of size $d$. We show that if a $k$-uniform hypergraph on $n$ vertices $\\mathcal H$ satisfies $\\delta_{k-1}(\\mathcal H)\\geq \\alpha n$ for some $\\alpha>1/2$, then for every $\\ell<k/2$ $\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3091","kind":"arxiv","version":2},"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"}