Zobrazeno 1 - 10
of 109
pro vyhledávání: '"CHARLIER, ÉMILIE"'
We consider Cantor real numeration system as a frame in which every non-negative real number has a positional representation. The system is defined using a bi-infinite sequence $\Beta=(\beta_n)_{n\in\Z}$ of real numbers greater than one. We introduce
Externí odkaz:
http://arxiv.org/abs/2312.13767
For an alternate base $\boldsymbol{\beta}=(\beta_0,\ldots,\beta_{p-1})$, we show that if all rational numbers in the unit interval $[0,1)$ have periodic expansions with respect to the $p$ shifts of $\boldsymbol{\beta}$, then the bases $\beta_0,\ldots
Externí odkaz:
http://arxiv.org/abs/2206.01810
Among all positional numeration systems, the widely studied Bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. In 1989, Bertrand-Mathis characterized them via representations in a real base $\beta$.
Externí odkaz:
http://arxiv.org/abs/2202.04938
The first aim of this article is to give information about the algebraic properties of alternate bases $\boldsymbol{\beta}=(\beta_0,\dots,\beta_{p-1})$ determining sofic systems. We show that a necessary condition is that the product $\delta=\prod_{i
Externí odkaz:
http://arxiv.org/abs/2202.03718
We generalize the greedy and lazy $\beta$-transformations for a real base $\beta$ to the setting of alternate bases $\boldsymbol{\beta}=(\beta_0,\ldots,\beta_{p-1})$, which were recently introduced by the first and second authors as a particular case
Externí odkaz:
http://arxiv.org/abs/2102.08627
Autor:
Charlier, Émilie, Cisternino, Célia
We introduce and study series expansions of real numbers with an arbitrary Cantor real base $\boldsymbol{\beta}=(\beta_n)_{n\in\mathbb{N}}$, which we call $\boldsymbol{\beta}$-representations. In doing so, we generalize both representations of real n
Externí odkaz:
http://arxiv.org/abs/2102.07722
Publikováno v:
In Journal of Number Theory January 2024 254:184-198
The notion of $b$-regular sequences was generalized to abstract numeration systems by Maes and Rigo in 2002. Their definition is based on a notion of $\mathcal{S}$-kernel that extends that of $b$-kernel. However, this definition does not allow us to
Externí odkaz:
http://arxiv.org/abs/2012.04969
Publikováno v:
Advances in Applied Mathematics 125 (2021) 102151
We consider numeration systems based on a $d$-tuple $\mathbf{U}=(U_1,\ldots,U_d)$ of sequences of integers and we define $(\mathbf{U},\mathbb{K})$-regular sequences through $\mathbb{K}$-recognizable formal series, where $\mathbb{K}$ is any semiring.
Externí odkaz:
http://arxiv.org/abs/2006.11126