{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T02:49:28Z","timestamp":1774320568107,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We study generalized small Schr\u00f6der paths in the sense of arbitrary sizes of steps. A generalized small Schr\u00f6der path is a generalized lattice path from $(0,0)$ to $(2n,0)$ with the step set of\u00a0 $\\{(k,k), (l,-l), (2r,0)\\, |\\, k,l,r \\in {\\bf P}\\}$, where ${\\bf P}$\u00a0is the set of positive integers, which never goes below the $x$-axis, and with no horizontal steps at level 0.\u00a0 We find a bijection between 5-colored Dyck paths and generalized small Schr\u00f6der paths, proving that the number of generalized small Schr\u00f6der paths is equal to $\\sum_{k=1}^{n} N(n,k)5^{n-k}$ for $n\\geq 1$.<\/jats:p>","DOI":"10.37236\/4827","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:24:36Z","timestamp":1578698676000},"source":"Crossref","is-referenced-by-count":3,"title":["Generalized Small Schr\u00f6der Numbers"],"prefix":"10.37236","volume":"22","author":[{"given":"JiSun","family":"Huh","sequence":"first","affiliation":[]},{"given":"SeungKyung","family":"Park","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,7,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:13:56Z","timestamp":1579256036000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i3p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,31]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/4827","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,31]]},"article-number":"P3.14"}}