Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Berthé, Valerie"'
In 1980, R. Tijdeman provided an on-line algorithm that generates sequences over a finite alphabet with minimal discrepancy, that is, such that the occurrence of each letter optimally tracks its frequency. In this article, we define discrete dynamica
Externí odkaz:
http://arxiv.org/abs/2405.08532
Autor:
Berthé, Valérie, Karimov, Toghrul, Nieuwveld, Joris, Ouaknine, Joël, Vahanwala, Mihir, Worrell, James
We investigate the decidability of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N};<,P_1, \ldots,P_k \rangle$, for various unary predicates $P_1,\ldots,P_k \subseteq \mathbb{N}$. We focus in particular on "arithmetic" predi
Externí odkaz:
http://arxiv.org/abs/2405.07953
This paper studies obstructions to preservation of return sets by episturmian morphisms. We show, by way of an explicit construction, that infinitely many obstructions exist. This generalizes and improves an earlier result about Sturmian morphisms.
Externí odkaz:
http://arxiv.org/abs/2404.08072
Autor:
Berthé, Valérie, Yassawi, Reem
Aperiodic order refers to the mathematical formalisation of quasicrystals. Substitutions and cut and project sets are among their main actors; they also play a key role in the study of dynamical systems, whether they are symbolic, generated by tiling
Externí odkaz:
http://arxiv.org/abs/2404.04116
Autor:
Berthé, Valérie, Goulet-Ouellet, Herman, Nyberg-Brodda, Carl-Fredrik, Perrin, Dominique, Petersen, Karl
The density of a rational language can be understood as the frequency of some "pattern" in the shift space, for example a pattern like "words with an even number of a given letter." We study the density of group languages, i.e. rational languages rec
Externí odkaz:
http://arxiv.org/abs/2403.17892
For which unary predicates $P_1, \ldots, P_m$ is the MSO theory of the structure $\langle \mathbb{N}; <, P_1, \ldots, P_m \rangle$ decidable? We survey the state of the art, leading us to investigate combinatorial properties of almost-periodic, morph
Externí odkaz:
http://arxiv.org/abs/2311.04895
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction. We discus
Externí odkaz:
http://arxiv.org/abs/2303.07777
Autor:
Berthé, Valérie, Puzynina, Svetlana
An infinite word generated by a substitution is rigid if all the substitutions which fix this word are powers of a same substitution. Sturmian words as well as characteristic Arnoux-Rauzy words are known to be rigid. In the present paper, we prove th
Externí odkaz:
http://arxiv.org/abs/2205.07707
We revisit the notion of one-sided recognizability of morphisms and its relation to two-sided recognizability.
Externí odkaz:
http://arxiv.org/abs/2204.03892
An S-adic system is a symbolic dynamical system generated by iterating an infinite sequence of substitutions or morphisms, called a directive sequence. A finitary S-adic dynamical system is one where the directive sequence consists of morphisms selec
Externí odkaz:
http://arxiv.org/abs/2202.07270