Abstract
Recently, Andrews and Yee studied two-variable generalizations of two identities involving partition functions \(p_\omega (n)\) and \(p_\nu (q)\) introduced by Andrews, Dixit and Yee. In this paper, we present a combinatorial proof of an interesting identity in their work.
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References
Andrews, G.E., Yee, A.J.: Some identities associated with mock theta functions \(\omega (q)\) and \(\nu (q)\) (2017). arXiv:1709.03213
Andrews, G.E., Dixit, A., Yee, A.J.: Partitions associated with the Ramanujan/Watson mock theta functions \(\omega (q)\), \(\nu (q)\) and \(\phi (q)\). Res. Number Theory 1, 19 (2015)
Andrews, G.E.: The Theory of Partitions, Encyclopedia of Mathematics and Its Applications, vol. 2. Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam (1976) (Reprinted: Cambridge University Press, London and New York, 1984)
Acknowledgements
I would like to thank George E. Andrews and Ae Ja Yee for many helpful discussions. I also want to thank the referee for the careful reading and helpful comments.
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Chern, S. Combinatorial proof of an identity of Andrews and Yee. Ramanujan J 49, 505–513 (2019). https://doi.org/10.1007/s11139-018-0012-0
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DOI: https://doi.org/10.1007/s11139-018-0012-0