On the combinatorics of the number of even parts in all partitions with distinct parts
type: Item
instance of: scholarly article
title: On the combinatorics of the number of even parts in all partitions with distinct parts
zbMATH Open document ID: 1489.11169
author: Runqiao Li
author: Andrew Y. Z. Wang
published in: The Ramanujan Journal
publication date: 2021-11-29T00:00:00Z
review text: 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.
reviewed by: Mircea Merca
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 7434823
zbMATH Keywords: even part
zbMATH Keywords: partition identity
zbMATH Keywords: bijection
MaRDI profile type: Publication
full work available at URL: s11139-020-00356-w
OpenAlex ID: W3130135699
cites work: On the number of even parts in all partitions of \(n\) into distinct parts
cites work: Combinatorial proofs of two theorems related to the number of even parts in all partitions of \(n\) into distinct parts
DOI: 10.1007/S11139-020-00356-W
description: scientific article; zbMATH DE number 7434823