Finite $\beta$-expansion of natural numbers

Abstract: If $\beta$ is an integer, then each $x \in \mathbb{Z}[1/\beta] \cap [0,\infty)$ has finite expansion in base $\beta$. As a generalization of this property for $\beta>1$, the condition (F$_{1}$) that each $x \in \mathbb{N}$ has finite $\beta$-expansion was proposed by Frougny and Solomyak. In this talk, we give a sufficient condition for (F$_{1}$). Moreover we also find $\beta$ with property (F$_{1}$) which does not have positive finiteness property.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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