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arXiv · 1611.05513

Dilated Floor Functions That Commute

Jeffrey C. Lagarias·Takumi Murayama·D. Harry Richman
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Abstract

We determine all pairs of real numbers $(\alpha, \beta)$ such that the dilated floor functions $\lfloor \alpha x\rfloor$ and $\lfloor \beta x\rfloor$ commute under composition, i.e., such that $\lfloor \alpha \lfloor \beta x\rfloor\rfloor = \lfloor \beta \lfloor \alpha x\rfloor\rfloor$ holds for all real $x$.

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Jeffrey C. Lagarias, Takumi Murayama, D. Harry Richman. 2016-11-17. Dilated Floor Functions That Commute. https://doi.org/10.4169/amer.math.monthly.123.10.1033

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