A Partition Identity Related to Stanley's Theorem

Mircea Merca; Maxie D. Schmidt

doi:10.1080/00029890.2018.1521232

A Partition Identity Related to Stanley's Theorem

Number Theory 2023-10-23 v1 Combinatorics

Authors: Mircea Merca , Maxie D. Schmidt

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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.

Keywords

partition identity euler's totient function lambert series euler's partition function stanley's theorem additive number theory

Cite

@article{arxiv.2310.13672,
  title  = {A Partition Identity Related to Stanley's Theorem},
  author = {Mircea Merca and Maxie D. Schmidt},
  journal= {arXiv preprint arXiv:2310.13672},
  year   = {2023}
}

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Preprint version of the article submitted for publication in 2017

A Partition Identity Related to Stanley's Theorem

Abstract

Keywords

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