On the Number of Even Parts in All Partitions of n into Distinct Parts

George E. Andrews, Mircea Merca

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)47-54
Number of pages8
JournalAnnals of Combinatorics
Volume24
Issue number1
DOIs
StatePublished - Mar 1 2020

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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