{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:22Z","timestamp":1753893862280,"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>A chord diagram is a set of chords of a circle such that no pair of chords has a common endvertex. A chord diagram $E$ with $n$ chords is called an $n$-crossing if all chords of $E$ are mutually crossing. A chord diagram $E$ is called nonintersecting if $E$ contains no $2$-crossing. For a chord diagram $E$ having a $2$-crossing $S = \\{ x_1 x_3, x_2 x_4 \\}$, the expansion of $E$ with respect to $S$ is to replace $E$ with $E_1 = (E \\setminus S) \\cup \\{ x_2 x_3, x_4 x_1 \\}$ or $E_2 = (E \\setminus S) \\cup \\{ x_1 x_2, x_3 x_4 \\}$. It is shown that there is a one-to-one correspondence between the multiset of all nonintersecting chord diagrams generated from an $n$-crossing with a finite sequence of expansions and the set of alternating permutations of order $n+1$.<\/jats:p>","DOI":"10.37236\/5120","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:14:40Z","timestamp":1578694480000},"source":"Crossref","is-referenced-by-count":3,"title":["Expansions of a Chord Diagram and Alternating Permutations"],"prefix":"10.37236","volume":"23","author":[{"given":"Tomoki","family":"Nakamigawa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2016,1,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:37:23Z","timestamp":1579239443000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5120","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,1,11]]},"article-number":"P1.7"}}