{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:54Z","timestamp":1753893774252,"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>Noting that cycle diagrams of permutations visually resemble grid diagrams used to depict knots and links in topology, we consider the knot (or link) obtained from the cycle diagram of a permutation. We show that the permutations which correspond in this way to an unknot are enumerated by the Schr\u00f6der numbers, and also enumerate the permutations corresponding to an unlink. The proof uses Bennequin's inequality.<\/jats:p>","DOI":"10.37236\/11016","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T07:46:23Z","timestamp":1662623183000},"source":"Crossref","is-referenced-by-count":1,"title":["Unknotted Cycles"],"prefix":"10.37236","volume":"29","author":[{"given":"Christopher","family":"Cornwell","sequence":"first","affiliation":[]},{"given":"Nathan","family":"McNew","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,9,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T07:46:24Z","timestamp":1662623184000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i3p50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,9]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/11016","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,9,9]]},"article-number":"P3.50"}}