Add to ORKGFor abstract numeration systems built on exponential regular languages (including those coming from substitutions), we show that the set of real numbers having an ultimately periodic representation is $\mathbb{Q}(\beta)$ if the dominating eigenvalue $\beta>1$ of the automaton accepting the language is a Pisot number. Moreover, if $\beta$ is neither a Pisot nor a Salem number, then there exist points in $\mathbb{Q}(\beta)$ which do not have any ultimately periodic representation
Abstract. This paper studies tilings and representation sapces related to the β-transformation when ...
Abstract. We study rational numbers with purely periodic Rényi β-expansions. For bases β satisfying ...
Generalizations of positional number systems in which N is recognizable by finite automata are obtai...
For abstract numeration systems built on exponential regular languages (including those coming from ...
Using a genealogically ordered infinite regular language, we know how to represent an interval of R....
AbstractUsing a genealogically ordered infinite regular language, we know how to represent an interv...
A beta expansion is the analogue of the base 10 representation of a real number, where the base may ...
Peoples over the ages use different counting systems. Appling that to cryptography, we use to repres...
International audienceWe study real numbers $\beta$ with the curious property that the $\beta$-expan...
This paper studies tilings related to the $\beta$-transformation when $\beta$ is a Pisot number (tha...
Abstract. For a (non-unit) Pisot number β, several collections of tiles are associated with β-numera...
International audienceFor a (non-unit) Pisot number $\beta$, several collections of tiles are associ...
It is well-known that real numbers with a purely periodic decimal expansion are the rationals having...
Abstract. Given a number β>1, the beta-transformation T = Tβ is defined for x ∈ [0,1] by Tx: = βx...
We study periodic expansions in positional number systems with a base β ∈ C, |β| > 1, and with coeff...
Abstract. This paper studies tilings and representation sapces related to the β-transformation when ...
Abstract. We study rational numbers with purely periodic Rényi β-expansions. For bases β satisfying ...
Generalizations of positional number systems in which N is recognizable by finite automata are obtai...
For abstract numeration systems built on exponential regular languages (including those coming from ...
Using a genealogically ordered infinite regular language, we know how to represent an interval of R....
AbstractUsing a genealogically ordered infinite regular language, we know how to represent an interv...
A beta expansion is the analogue of the base 10 representation of a real number, where the base may ...
Peoples over the ages use different counting systems. Appling that to cryptography, we use to repres...
International audienceWe study real numbers $\beta$ with the curious property that the $\beta$-expan...
This paper studies tilings related to the $\beta$-transformation when $\beta$ is a Pisot number (tha...
Abstract. For a (non-unit) Pisot number β, several collections of tiles are associated with β-numera...
International audienceFor a (non-unit) Pisot number $\beta$, several collections of tiles are associ...
It is well-known that real numbers with a purely periodic decimal expansion are the rationals having...
Abstract. Given a number β>1, the beta-transformation T = Tβ is defined for x ∈ [0,1] by Tx: = βx...
We study periodic expansions in positional number systems with a base β ∈ C, |β| > 1, and with coeff...
Abstract. This paper studies tilings and representation sapces related to the β-transformation when ...
Abstract. We study rational numbers with purely periodic Rényi β-expansions. For bases β satisfying ...
Generalizations of positional number systems in which N is recognizable by finite automata are obtai...
