Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2403.04342 |
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Inhaltsangabe:
- An approximate divisor order is a partial order on the positive integers $\mathbb{N}^+$ that refines the divisor order and is refined by the additive total order. A previous paper studied such a partial order on $\mathbb{N}^+$, produced using the floor function. A positive integer $d$ is a floor quotient of $n$, denoted $d \,\preccurlyeq_{1}\, n$, 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 a family of partial orders, the $a$-floor quotient relations $\,\preccurlyeq_{a}\,$, for $a \in \mathbb{N}^+$, which interpolate between the floor quotient order and the divisor order on $\mathbb{N}^+$. The paper studies the internal structure of these orders.