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Enumerative proofs of certain q-identities

Published online by Cambridge University Press:  18 May 2009

George E. Andrews
Affiliation:
The Pennsylvania State University University Park, Pennsylvania
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Many q-identities have been proved combinatorially. For example

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

References

1.Andrews, G. E., On basic hypergeometric series, mock theta functions, and partitions (II); to appear.Google Scholar
2.Cheema, M. S., Vector partitions and combinatorial identities, Math. Comp. 18 (1964), 414420.CrossRefGoogle Scholar
3.Hardy, G. H., Ramanujan (Cambridge University Press, Cambridge, 1940).Google Scholar
4.Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (Oxford University Press, London, 4th ed., 1960).Google Scholar
5.Heine, E., Handbuch der Kugelfunctionen, Band I (Berlin, 1878).Google Scholar
6.Ramanujan, S., Collected works (Cambridge University Press, Cambridge, 1927).Google Scholar
7.Slater, L. J., Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 54 (1952), 147167.CrossRefGoogle Scholar
8.Sylvester, J. J., A constructive theory of partitions, etc., Collected math, papers IV (Cambridge, 1912), 3436.Google Scholar
9.Watson, G. N., The mock theta functions (II), Proc. London Math. Soc. (2) 42 (1937), 274304.CrossRefGoogle Scholar
10.Wright, E. M., An enumerative proof of an identity of Jacobi, J. London Math. Soc. 40 (1965), 5557.CrossRefGoogle Scholar