{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:28Z","timestamp":1753893808276,"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>The Alladi-Gordon identity $\\sum_{k=0}^{j}(q^{i-k+1};q)_k\\, {j \\brack k} q^{(i-k)(j-k)}=1$ plays an important role for the Alladi-Gordon generalization of Schur's partition theorem. By using Joichi-Stanton's insertion algorithm, we present an overpartition interpretation for the Alladi-Gordon key identity. Based on this interpretation, we further obtain a combinatorial proof of the Alladi-Gordon key identity by establishing an involution on the underlying set of overpartitions.<\/jats:p>","DOI":"10.37236\/2826","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:56:50Z","timestamp":1578693410000},"source":"Crossref","is-referenced-by-count":0,"title":["An Involution Proof of the Alladi-Gordon Key Identity for Schur's Partition Theorem"],"prefix":"10.37236","volume":"20","author":[{"given":"James J.Y.","family":"Zhao","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,3,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p63\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p63\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:25:07Z","timestamp":1579242307000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p63"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2826","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,3,24]]},"article-number":"P63"}}