{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:11Z","timestamp":1753893851005,"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>Using the Algorithm Z developed by Zeilberger, we give a combinatorial proof of the following $q$-binomial coefficient identity $$ \\sum_{k=0}^m(-1)^{m-k}{m\\brack k}{n+k\\brack a}(-xq^a;q)_{n+k-a}q^{{k+1\\choose 2}-mk+{a\\choose 2}} $$ $$=\\sum_{k=0}^n{n\\brack k}{m+k\\brack a}x^{m+k-a}q^{mn+{k\\choose 2}}, $$ which was obtained by Hou and Zeng [European J. Combin. 28 (2007), 214\u2013227].<\/jats:p>","DOI":"10.37236\/462","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:16:50Z","timestamp":1578716210000},"source":"Crossref","is-referenced-by-count":0,"title":["Combinatorial Proof of a Curious $q$-Binomial Coefficient Identity"],"prefix":"10.37236","volume":"17","author":[{"given":"Victor J. W.","family":"Guo","sequence":"first","affiliation":[]},{"given":"Jiang","family":"Zeng","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,2,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:59:13Z","timestamp":1579305553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1n13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/462","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,2,8]]},"article-number":"N13"}}