Abstract
Recently, George Andrews gave a detailed study of partitions with even parts below odd parts in which only the largest even part appears an odd number of times. In this note, we provide a combinatorial proof of a generating function identity related to such partitions. This answers a problem of Andrews.
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References
Andrews, G.E.: Integer partitions with even parts below odd parts and the mock theta functions. Ann. Comb. 22(3), 433–445 (2018)
Gasper, G., Rahman, M.: Basic hypergeometric series, 2nd edn. Encyclopedia of Mathematics and its Applications, vol. 96. Cambridge University Press, Cambridge, pp. xxvi+428 (2004)
Kim, B.: Combinatorial proofs of certain identities involving partial theta functions. Int. J. Number Theory 6(2), 449–460 (2010)
Acknowledgements
I would like to thank George E. Andrews for helpful discussions.
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Chern, S. On a problem of George Andrews concerning partitions with even parts below odd parts. Afr. Mat. 30, 691–695 (2019). https://doi.org/10.1007/s13370-019-00676-1
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DOI: https://doi.org/10.1007/s13370-019-00676-1