24 citations · 51 across the 8 of their papers we have counts for
9 papers
A Numeration System for Fibonacci-like Wang Shifts
Sébastien Labbé, Jana Lepšová
Motivated by the study of Fibonacci-like Wang shifts, we define a numeration system for and based on the binary alphabet . We introduce a set o…
Almost everywhere balanced sequences of complexity
Julien Cassaigne, Sébastien Labbé, Julien Leroy
We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The algorithm is defined by two matrices and we show that…
Three characterizations of a self-similar aperiodic 2-dimensional subshift
Sébastien Labbé
The goal of this chapter is to illustrate a generalization of the Fibonacci word to the case of 2-dimensional configurations on . More precisely, we consider a partic…
Rauzy induction of polygon partitions and toral -rotations
Sébastien Labbé
We extend the notion of Rauzy induction of interval exchange transformations to the case of toral -rotation, i.e., -action defined by rotations on a 2-t…
Markov partitions for toral -rotations featuring Jeandel-Rao Wang shift and model sets
Sébastien Labbé
We define a partition and a -rotation (-action defined by rotations) on a 2-dimensional torus whose associated symbolic dynamical system…
A note on matrices mapping a positive vector onto its element-wise inverse
Sébastien Labbé
For any primitive matrix with positive diagonal entries, we prove the existence and uniqueness of a positive vector such…
A Perron theorem for matrices with negative entries and applications to Coxeter groups
Jean-Philippe Labbé, Sébastien Labbé
Handelman (J. Operator Theory, 1981) proved that if the spectral radius of a matrix is a simple root of the characteristic polynomial and is strictly greater than the modulus o…
On some symmetric multidimensional continued fraction algorithms
Pierre Arnoux, Sébastien Labbé
We compute explicitly the density of the invariant measure for the Reverse algorithm which is absolutely continuous with respect to Lebesgue measure, using a method proposed by Arn…
Complexity of the Fibonacci snowflake
Alexandre Blondin Massé, Srečko Brlek, Sébastien Labbé +1
The object under study is a particular closed curve on the square lattice related with the Fibonacci sequence . It belongs to a class of curves whose length is $4F_{3n+…