Geodesic
The \(q\)-binomial theorem and two symmetric \(q\)-identities
The electronic journal of combinatorics, Tome 10 (2003)
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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.
DOI : 10.37236/1727
Classification : 05A19, 05A30, 05A17 
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     author = {Victor J. W. Guo},
     title = {The \(q\)-binomial theorem and two symmetric \(q\)-identities},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1727},
     zbl = {1023.05016},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1727/}
}
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Victor J. W. Guo. The \(q\)-binomial theorem and two symmetric \(q\)-identities. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1727

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