{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813201,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Large Schr\u00f6der\u00a0paths, sparse noncrossing partitions, partial horizontal strips, and\u00a0$132$-avoiding alternating sign matrices are objects enumerated by Schr\u00f6der\u00a0numbers.\u00a0In this paper we give formula for the number of Schr\u00f6der\u00a0objects with given type\u00a0and number of connected components.\u00a0The proofs are bijective using Chung-Feller style.\u00a0A bijective proof for the number of Schr\u00f6der\u00a0objects with given type is provided.\u00a0We also give a combinatorial interpretation for the number of small Schr\u00f6der\u00a0paths.<\/jats:p>","DOI":"10.37236\/5659","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:09:41Z","timestamp":1578690581000},"source":"Crossref","is-referenced-by-count":0,"title":["Chung-Feller Property of Schr\u00f6der Objects"],"prefix":"10.37236","volume":"23","author":[{"given":"Youngja","family":"Park","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sangwook","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2016,5,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:28:31Z","timestamp":1579238911000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5659","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,5,13]]},"article-number":"P2.34"}}