{"paper":{"title":"An Erd{\\H o}s-Ko-Rado theorem for permutations with fixed number of cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cheng Yeaw Ku, Kok Bin Wong","submitted_at":"2014-02-04T09:26:47Z","abstract_excerpt":"Let $S_{n}$ denote the set of permutations of $[n]=\\{1,2,\\dots, n\\}$. For a positive integer $k$, define $S_{n,k}$ to be the set of all permutations of $[n]$ with exactly $k$ disjoint cycles, i.e., \\[ S_{n,k} = \\{\\pi \\in S_{n}: \\pi = c_{1}c_{2} \\cdots c_{k}\\},\\] where $c_1,c_2,\\dots ,c_k$ are disjoint cycles. The size of $S_{n,k}$ is given by $\\left [ \\begin{matrix}n\\\\ k \\end{matrix}\\right]=(-1)^{n-k}s(n,k)$, where $s(n,k)$ is the Stirling number of the first kind. A family $\\mathcal{A} \\subseteq S_{n,k}$ is said to be $t$-{\\em intersecting} if any two elements of $\\mathcal{A}$ have at least $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0668","kind":"arxiv","version":1},"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"}