{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833298,"version":"3.41.2"},"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 give bijective proofs that, when combined with one of the combinatorial proofs of the general ballot formula, constitute a combinatorial argument yielding the number of lattice paths from $(0,0)$ to $(n,rn)$ that touch or cross the diagonal $y = rx$ at exactly $k$ lattice points. \u00a0This enumeration partitions all lattice paths from $(0,0)$ to $(n,rn)$. \u00a0While the resulting formula can be derived using results from Niederhausen, the bijections and combinatorial proof are new.<\/jats:p>","DOI":"10.37236\/2477","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:24:22Z","timestamp":1578713062000},"source":"Crossref","is-referenced-by-count":2,"title":["Enumerating Lattice Paths Touching or Crossing the Diagonal at a Given Number of Lattice Points"],"prefix":"10.37236","volume":"19","author":[{"given":"Michael Z.","family":"Spivey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,8,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:31:20Z","timestamp":1579300280000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i3p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,7,12]]}},"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.37236\/2477","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,8,30]]},"article-number":"P24"}}