{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:19:12Z","timestamp":1759335552194,"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>An elevated Schr\u00f6der path is a lattice path that uses the steps $(1,1)$, $(1,-1)$, and $(2,0)$, that begins and ends on the $x$-axis, and that remains strictly above the $x$-axis otherwise. The total area of elevated Schr\u00f6der paths  of length $2n+2$ satisfies the recurrence  $f_{n+1}=6f_n-f_{n-1}$, $n \\geq 2$, with the initial conditions $f_0=1$, $f_1=7$. A combinatorial interpretation of this recurrence is given, by first  introducing sets of unrestricted paths whose cardinality also satisfies the recurrence relation and then   establishing a bijection between the set of these paths and the set of triangles constituting the total area of elevated Schr\u00f6der paths.<\/jats:p>","DOI":"10.37236\/1472","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T01:31:33Z","timestamp":1578619893000},"source":"Crossref","is-referenced-by-count":8,"title":["A Combinatorial Interpretation of the Area of Schr\u00f6der Paths"],"prefix":"10.37236","volume":"6","author":[{"given":"E.","family":"Pergola","sequence":"first","affiliation":[]},{"given":"R.","family":"Pinzani","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,10,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:32:04Z","timestamp":1579307524000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,10,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1472","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,10,14]]},"article-number":"R40"}}