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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Vydáno v:arXiv.org
Hlavní autoři: Merca, Mircea, Schmidt, Maxie D
Médium: Paper
Jazyk:angličtina
Vydáno: Ithaca Cornell University Library, arXiv.org 20.10.2023
Témata:
Number theory
Partitions (mathematics)
ISSN:2331-8422
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Abstract 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.
AbstractList 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.
Author Schmidt, Maxie D
Merca, Mircea
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Snippet 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...
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Partitions (mathematics)
Title A Partition Identity Related to Stanley's Theorem
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