{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:59Z","timestamp":1753893839262,"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>Symmetric joint distribution between crossings and nestings was established in several combinatorial objects. Recently, Marberg extended Chen and Guo's result on coloured matchings to coloured set partitions following a multi-dimensional generalization of the bijection and enumerative methods from Chen, Deng, Du, Stanley, and Yan. We complete the study for arc-coloured permutations by establishing symmetric joint distribution for crossings and nestings and by showing that the ordinary generating functions for $j$-noncrossing, $k$-nonnesting, $r$-coloured permutations according to size $n$ are rational functions. Finally, we automate the generation of these rational functions and analyse the first $70$ series.<\/jats:p>","DOI":"10.37236\/4080","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:33:16Z","timestamp":1578702796000},"source":"Crossref","is-referenced-by-count":0,"title":["Crossings and Nestings  for Arc-Coloured Permutations and Automation"],"prefix":"10.37236","volume":"22","author":[{"given":"Lily","family":"Yen","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,1,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:38:42Z","timestamp":1579257522000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4080","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,1,20]]},"article-number":"P1.14"}}