{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822970,"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>Let $S_n$ be the set of all permutations on $[n]:=\\{1,2,\\ldots,n\\}$. We denote by $\\kappa_n$ the smallest cardinality of a subset ${\\cal A}$ of $S_{n+1}$ that \"covers\" $S_n$, in the sense that each $\\pi\\in S_n$ may be found as an order-isomorphic subsequence of some $\\pi'$ in ${\\cal A}$. \u00a0What are general upper bounds on $\\kappa_n$? \u00a0If we randomly select $\\nu_n$ elements of $S_{n+1}$, when does the probability that they cover $S_n$ transition from 0 to 1? \u00a0Can we provide a fine-magnification analysis that provides the \"probability of coverage\" \u00a0when $\\nu_n$ is around the level given by the phase transition? \u00a0 In this paper we answer these questions and raise others.<\/jats:p>","DOI":"10.37236\/2168","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:00:47Z","timestamp":1578711647000},"source":"Crossref","is-referenced-by-count":0,"title":["Covering n-Permutations with (n+1)-Permutations"],"prefix":"10.37236","volume":"20","author":[{"given":"Taylor F","family":"Allison","sequence":"first","affiliation":[]},{"given":"Anant P","family":"Godbole","sequence":"additional","affiliation":[]},{"given":"Kathryn M","family":"Hawley","sequence":"additional","affiliation":[]},{"given":"Bill","family":"Kay","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,1,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:20:34Z","timestamp":1579299634000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2168","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,1,14]]},"article-number":"P6"}}