{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:29:32Z","timestamp":1773275372849,"version":"3.50.1"},"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>We show that matchings avoiding a certain partial pattern are counted by the $3$-Catalan numbers. We give a characterization of $12312$-avoiding matchings in terms of restrictions on the corresponding oscillating tableaux. We also find a bijection between matchings avoiding both patterns $12312$ and $121323$ and Schr\u00f6der paths without peaks at level one, which are counted by the super-Catalan numbers or the little Schr\u00f6der numbers. A refinement of the super-Catalan numbers is derived by fixing the number of crossings in the matchings. In the sense of Wilf-equivalence, we use the method of generating trees to show that the patterns 12132, 12123, 12321, 12231, 12213 are all equivalent to the pattern $12312$.<\/jats:p>","DOI":"10.37236\/1138","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:55:12Z","timestamp":1578700512000},"source":"Crossref","is-referenced-by-count":3,"title":["Matchings Avoiding Partial Patterns"],"prefix":"10.37236","volume":"13","author":[{"given":"William Y. C.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Toufik","family":"Mansour","sequence":"additional","affiliation":[]},{"given":"Sherry H. F.","family":"Yan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,12,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r112\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r112\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:05:37Z","timestamp":1579302337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1138","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12,18]]},"article-number":"R112"}}