A Partition Identity Related to Stanley's Theorem

In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of \(1\)'s in the partitions of \(n\). A new expansion for Euler's partition function \(p(n)\) is derived in this context. These surprising new results...

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Vydané v:	arXiv.org
Hlavní autori:	Merca, Mircea, Schmidt, Maxie D
Médium:	Paper
Jazyk:	English
Vydavateľské údaje:	Ithaca Cornell University Library, arXiv.org 20.10.2023
Predmet:	Number theory Partitions (mathematics)
ISSN:	2331-8422
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Shrnutí:	In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of \(1\)'s in the partitions of \(n\). A new expansion for Euler's partition function \(p(n)\) is derived in this context. These surprising new results connect the famous classical totient function from multiplicative number theory to the additive theory of partitions.
Bibliografia:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2310.13672