Rooted partitions and number-theoretic functions
Number Theory
2023-10-31 v1
Abstract
Recently, Merca and Schmidt proved a number of identities relating partitions of an integer with two classic number-theoretic functions, namely the M\"obius function and Euler's totient function. Their demonstrations were mainly algebraic. We give bijective proofs of some of these results. Our main tools are the concept of a rooted partition and an operation which we call the direct sum of a partition and a rooted partition.
Keywords
Cite
@article{arxiv.2310.19098,
title = {Rooted partitions and number-theoretic functions},
author = {Bruce Sagan},
journal= {arXiv preprint arXiv:2310.19098},
year = {2023}
}
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10 pages