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arXiv · 2212.11689

The floor quotient partial order

Jeffery C. Lagarias·David Harry Richman
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Abstract

A positive integer $d$ is a floor quotient of $n$ if there is a positive integer $k$ such that $d = \lfloor n/k \rfloor$. 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.

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Jeffery C. Lagarias, David Harry Richman. 2022-12-22. The floor quotient partial order. https://doi.org/10.1016/j.aam.2023.102615

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