{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T23:34:21Z","timestamp":1773444861697,"version":"3.50.1"},"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>We give a combinatorial proof of an identity that involves Eulerian numbers and was obtained algebraically by Brenti and Welker (2009). To do so, we use alcoved triangulations of dilated hypersimplices. As a byproduct, we describe the dual graph of the triangulation in the case of the dilated standard simplex and the hypersimplex, conjecture its structure for dilated hypersimplices. Also, we give a new proof of the classical result that the Eulerian numbers coincide with the normalized volumes of the hypersimplices.<\/jats:p>","DOI":"10.37236\/14377","type":"journal-article","created":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:22:01Z","timestamp":1773440521000},"source":"Crossref","is-referenced-by-count":0,"title":["A Combinatorial Proof of an Identity Involving Eulerian Numbers"],"prefix":"10.37236","volume":"33","author":[{"given":"Jer\u00f3nimo","family":"Valencia Porras","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,3,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:22:09Z","timestamp":1773440529000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/14377","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,13]]},"article-number":"P1.52"}}