On the combinatorics of the number of even parts in all partitions with distinct parts
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. \textit{G. E. Andrews} and the reviewer [Ann. Comb. 24, No. 1, 47--54 (2020; Zbl 1473.11190)] studied the number of even parts in all partitions of \(n\) and obtained some interesting properties. \textit{C. Ballantine} and the reviewer [Ramanujan J. 54, No. 1, 107--112 (2021; Zbl 1462.05027)] provided purely combinatorial proofs of these results. In this paper the author provided new bijective proofs of these identities introduced by Andrews and the reviewer.
scientific article; zbMATH DE number 7434823