descriptionPublicationkeyboard_double_arrow_right Article , Preprint 26 Nov 2018Embargo end date: 01 Jan 2023 English Publisher:Informa UK LimitedJournal:The American Mathematical Monthly, volume 125, pages 929-933 (issn: 0002-9890, eissn: 1930-0972,

Authors: Mircea Merca; Maxie D. Schmidt;

doi: 10.1080/00029890.2018.1521232 , 10.48550/arxiv.2310.13672

arXiv: http://arxiv.org/abs/2310.13672

A Partition Identity Related to Stanley’s Theorem

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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.

Preprint version of the article submitted for publication in 2017

Related Organizations

Georgia Institute of Technology
United States
Academy of Romanian Scientists
Romania

Keywords

Mathematics - Number Theory, FOS: Mathematics, 05A17, 11B75, 11P81, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO)

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