{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T03:46:25Z","timestamp":1773891985706,"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>In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the $LDU$ decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition formula for weighted large Schr\u00f6der paths.<\/jats:p>","DOI":"10.37236\/4793","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:16:15Z","timestamp":1578694575000},"source":"Crossref","is-referenced-by-count":3,"title":["Combinatorial Proofs of Addition Formulas"],"prefix":"10.37236","volume":"23","author":[{"given":"Xiang-Ke","family":"Chang","sequence":"first","affiliation":[]},{"given":"Xing-Biao","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Hongchuan","family":"Lei","sequence":"additional","affiliation":[]},{"given":"Yeong-Nan","family":"Yeh","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,1,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:37:29Z","timestamp":1579239449000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/4793","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,11]]},"article-number":"P1.8"}}