{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:04:39Z","timestamp":1758823479221,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A permutation $\\sigma\\in S_n$ is a $k$-separator if all of its patterns of length $k$ are distinct. Let $F(k)$ denote the maximal length of a $k$-separator. Hegarty (2013) showed that $k+\\left\\lfloor\\sqrt{2k-1}\\right\\rfloor-1\\leq F(k)\\leq k+\\left\\lfloor\\sqrt{2k-3}\\right\\rfloor$, and conjectured that $F(k)=k+\\left\\lfloor\\sqrt{2k-1}\\right\\rfloor-1$. This paper will strengthen the upper bound to prove the conjecture for all sufficiently large $k$ (in particular, for all $k\\geq 320801$).<\/jats:p>","DOI":"10.37236\/3765","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:56:43Z","timestamp":1578704203000},"source":"Crossref","is-referenced-by-count":1,"title":["The Maximal Length of a $k$-Separator Permutation"],"prefix":"10.37236","volume":"21","author":[{"given":"Benjamin","family":"Gunby","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,8,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:49:52Z","timestamp":1579258192000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i3p19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,6]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,7,3]]}},"URL":"https:\/\/doi.org\/10.37236\/3765","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,8,6]]},"article-number":"P3.19"}}