On the Number of Even Parts in All Partitions of \(\varvec{n}\) into Distinct Parts

  • George E. AndrewsEmail author
  • Mircea Merca


A famous theorem of Euler asserts that there are as many partitions of n into distinct parts as there are partitions into odd parts. The even parts in partitions of n into distinct parts play an important role in the Euler–Glaisher bijective proof of this result. In this paper, we investigate the number of even parts in all partitions of n into distinct parts providing new combinatorial interpretations for this number.


Combinatorial identity Euler’s partition identity Partitions 

Mathematics Subject Classification

Primary 11P83 Secondary 05A17 05A19 



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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsThe Pennsylvania State UniversityState CollegeUSA
  2. 2.Academy of Romanian ScientistsBucharestRomania

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