The floor quotient partial order
Number Theory
2025-09-03 v2
Abstract
A positive integer is a floor quotient of if there is a positive integer such that . The floor quotient relation defines a partial order on the positive integers. This paper studies the internal structure of this partial order and its M\"{o}bius function.
Cite
@article{arxiv.2212.11689,
title = {The floor quotient partial order},
author = {Jeffery C. Lagarias and David Harry Richman},
journal= {arXiv preprint arXiv:2212.11689},
year = {2025}
}
Comments
38 pages, 7 figures. v2: final version, to appear in Advances in Applied Mathematics