{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:58Z","timestamp":1753893838502,"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>In this paper we enumerate the number of $(k, r)$-Fuss-Schr\u00f6der paths of type $\\lambda$. Y. Park and S. Kim studied small Schr\u00f6der paths with type $\\lambda$. Generalizing the results to small $(k, r)$-Fuss-Schr\u00f6der paths with type $\\lambda$, we give a combinatorial interpretation for the number of small $(k, r)$-Fuss-Schr\u00f6der paths of type $\\lambda$ by using Chung-Feller style. We also give two sets of sparse noncrossing partitions of $[2(k + 1)n + 1]$ and $[2(k + 1)n + 2]$ which are in bijection with the set of all small and large, respectively, $(k, r)$-Fuss-Schr\u00f6der paths of type $\\lambda$.<\/jats:p>","DOI":"10.37236\/6719","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:54:50Z","timestamp":1578671690000},"source":"Crossref","is-referenced-by-count":1,"title":["Enumeration of Fuss-Schr\u00f6der paths"],"prefix":"10.37236","volume":"24","author":[{"given":"Suhyung","family":"An","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JiYoon","family":"Jung","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sangwook","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2017,6,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p30\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:56:42Z","timestamp":1579237002000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i2p30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,2]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6719","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,6,2]]},"article-number":"P2.30"}}