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

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Abstract

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.

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Correspondence to George E. Andrews.

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Andrews, G.E., Merca, M. On the Number of Even Parts in All Partitions of \(\varvec{n}\) into Distinct Parts. Ann. Comb. (2020). https://doi.org/10.1007/s00026-019-00479-y

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Keywords

  • Combinatorial identity
  • Euler’s partition identity
  • Partitions

Mathematics Subject Classification

  • Primary 11P83
  • Secondary 05A17
  • 05A19