{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:14Z","timestamp":1753893794724,"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>We notice two symmetric $q$-identities, which are special cases of the transformations of $_2\\phi_1$ series in Gasper and Rahman's book (Basic Hypergeometric Series, Cambridge  University Press, 1990, p. 241). In this paper, we give combinatorial proofs of these two identities and the $q$-binomial theorem by using conjugation of $2$-modular diagrams.<\/jats:p>","DOI":"10.37236\/1727","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T02:03:20Z","timestamp":1578621800000},"source":"Crossref","is-referenced-by-count":3,"title":["The $q$-Binomial Theorem and two Symmetric $q$-Identities"],"prefix":"10.37236","volume":"10","author":[{"given":"Victor J. W.","family":"Guo","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2003,9,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:06:56Z","timestamp":1579306016000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,9,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1727","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,9,12]]},"article-number":"R34"}}