{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T19:58:14Z","timestamp":1769198294847,"version":"3.49.0"},"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 $q$-analogue of some binomial coefficient identities of Y. Sun [Electron. J. Combin. 17 (2010), #N20] as follows: \\begin{align*} \\sum_{k=0}^{\\lfloor n\/2\\rfloor}{m+k\\brack k}_{q^2}{m+1\\brack n-2k}_{q} q^{n-2k\\choose 2} &amp;={m+n\\brack n}_{q}, \\\\ \\sum_{k=0}^{\\lfloor n\/4\\rfloor}{m+k\\brack k}_{q^4}{m+1\\brack n-4k}_{q} q^{n-4k\\choose 2} &amp;=\\sum_{k=0}^{\\lfloor n\/2\\rfloor}(-1)^k{m+k\\brack k}_{q^2}{m+n-2k\\brack n-2k}_{q}, \\end{align*} where ${n\\brack k}_q$ stands for the $q$-binomial coefficient. We provide two proofs, one of which is combinatorial via partitions.<\/jats:p>","DOI":"10.37236\/565","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:51:37Z","timestamp":1578714697000},"source":"Crossref","is-referenced-by-count":4,"title":["A $q$-Analogue of some Binomial Coefficient Identities of Y. Sun"],"prefix":"10.37236","volume":"18","author":[{"given":"Victor J. W.","family":"Guo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dan-Mei","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p78\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p78\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:14:33Z","timestamp":1579302873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p78"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/565","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,31]]},"article-number":"P78"}}