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On a problem of George Andrews concerning partitions with even parts below odd parts

  • Shane ChernEmail author
Article
  • 41 Downloads

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.

Keywords

Partition Generating function Combinatorial proof 

Mathematics Subject Classification

Primary 05A17 

Notes

Acknowledgements

I would like to thank George E. Andrews for helpful discussions.

References

  1. 1.
    Andrews, G.E.: Integer partitions with even parts below odd parts and the mock theta functions. Ann. Comb. 22(3), 433–445 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    Kim, B.: Combinatorial proofs of certain identities involving partial theta functions. Int. J. Number Theory 6(2), 449–460 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPenn State UniversityUniversity ParkUSA

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