{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821941,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the following generalization of the seminal Erd\u0151s\u2013Ko\u2013Rado theorem, due to Frankl. For some $k\\geq 2$, let $\\mathcal{F}$ be a $k$-wise intersecting family of $r$-subsets of an $n$ element set $X$, i.e. for any $F_1,\\ldots,F_k\\in \\mathcal{F}$, $\\cap_{i=1}^k F_i\\neq \\emptyset$. If $r\\leq \\dfrac{(k-1)n}{k}$, then $|\\mathcal{F}|\\leq {n-1 \\choose r-1}$. We prove a stability version of this theorem, analogous to similar results of Dinur-Friedgut, Keevash-Mubayi and others for the EKR theorem. The technique we use is a generalization of Katona's circle method, initially employed by Keevash, which uses expansion properties of a particular Cayley graph of the symmetric group.<\/jats:p>","DOI":"10.37236\/602","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:47:19Z","timestamp":1578714439000},"source":"Crossref","is-referenced-by-count":0,"title":["Stability Analysis for $k$-wise Intersecting Families"],"prefix":"10.37236","volume":"18","author":[{"given":"Vikram","family":"Kamat","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,5,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p115\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p115\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:11:51Z","timestamp":1579302711000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/602","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,5,16]]},"article-number":"P115"}}