{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:22Z","timestamp":1753893802600,"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>Let ${\\cal G}_n$ denote the set of lattice paths from $(0,0)$ to $(n,n)$ with steps of the form $(i,j)$ where $i$ and $j$ are nonnegative integers, not both zero.  Let ${\\cal D}_n$ denote the set of paths in ${\\cal G}_n$ with steps restricted to $(1,0),(0,1),(1,1)$, the so-called Delannoy paths. Stanley has shown that $| {\\cal G}_n | =2^{n-1}|{\\cal D}_n|$ and Sulanke has given a bijective proof. Here we give a simple statistic on ${\\cal G}_n$ that is uniformly distributed over the $2^{n-1}$ subsets of $[n-1]=\\{1,2,\\ldots,n\\}$ and takes the value $[n-1]$ precisely on the Delannoy paths.<\/jats:p>","DOI":"10.37236\/1835","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:31:15Z","timestamp":1578709875000},"source":"Crossref","is-referenced-by-count":0,"title":["A Uniformly Distributed Statistic on a Class of Lattice Paths"],"prefix":"10.37236","volume":"11","author":[{"given":"David","family":"Callan","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,11,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r82\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:52:54Z","timestamp":1579323174000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1835","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,11,16]]},"article-number":"R82"}}