{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:10Z","timestamp":1759335790865,"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>In this paper, we consider matchings avoiding partial patterns $1123$ and $1132$.  We give a bijection between $1123$-avoiding matchings with $n$ edges and nonnegative lattice paths from $(0,2)$ to $(2n,0)$. As a consequence, the refined enumeration of $1123$-avoiding matchings can be reduced to the enumeration of certain lattice paths. Another result of this paper is a bijection between $1132$-avoiding matchings with $n$ edges and lattice paths from $(0,0)$ to $(2n,0)$ starting with an up step, which may go under the $x$-axis.<\/jats:p>","DOI":"10.37236\/1115","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:56:27Z","timestamp":1578718587000},"source":"Crossref","is-referenced-by-count":1,"title":["Matchings Avoiding Partial Patterns and Lattice Paths"],"prefix":"10.37236","volume":"13","author":[{"given":"V\u00edt","family":"Jel\u00ednek","sequence":"first","affiliation":[]},{"given":"Nelson Y.","family":"Li","sequence":"additional","affiliation":[]},{"given":"Toufik","family":"Mansour","sequence":"additional","affiliation":[]},{"given":"Sherry H. F.","family":"Yan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,10,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r89\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r89\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:07:25Z","timestamp":1579320445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r89"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1115","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,10,19]]},"article-number":"R89"}}