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

George E. Andrews; Mircea Merca

doi:10.1007/s00026-019-00479-y

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

George E. Andrews, Mircea Merca

Mathematics

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13 Scopus citations

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 language	English (US)
Pages (from-to)	47-54
Number of pages	8
Journal	Annals of Combinatorics
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s00026-019-00479-y
State	Published - Mar 1 2020

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1007/s00026-019-00479-y

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

Abstract

All Science Journal Classification (ASJC) codes

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