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Combinatorial proofs of two theorems related to the number of even parts in all partitions of n into distinct parts

  • Cristina BallantineEmail author
  • Mircea Merca
Article
  • 36 Downloads

Abstract

Recently, Andrews and Merca considered the number of even parts in all partitions of n into distinct parts and obtained new combinatorial interpretations for this number. Their proofs rely on generating functions. In this paper, we provide purely combinatorial proofs of these results.

Keyword

Partitions 

Mathematics Subject Classification

05A17 11P83 

Notes

Acknowledgements

We are thankful to an anonymous referee for suggesting a clarification of one of the proofs.

References

  1. 1.
    Andrews, G.E., Merca, M.: On the number of even parts in all partitions of \(n\) into distinct parts, preprintGoogle Scholar
  2. 2.
    Ballantine, C., Bielak, R.: Combinatorial proofs of two Euler type identities due to Andrews. arXiv:1803.06394 (2018)
  3. 3.
    Fu, S., Tang, D.: Generalizing a partition theorem of Andrews. Math. Student 86(3–4), 91–96 (2017)MathSciNetGoogle Scholar
  4. 4.
    Pak, I.: Partition bijections, a survey. Ramanujan J. 12(1), 5–75 (2006)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceCollege of The Holy CrossWorcesterUSA
  2. 2.Academy of Romanian ScientistsBucharestRomania

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