5 papers
On the conjugates of Christoffel words
Y. Bugeaud, C. Reutenauer
We introduce a parametrization of the conjugates of Christoffel words based on the integer Ostrowski numeration system. We use it to give a precise description of the borders (pref…
Pairs of intertwined integer sequences
Christian Kassel, Christophe Reutenauer
In previous work we computed the number of ideals of codimension of the algebra of two-variable Laurent polynomials over a finite…
Christoffel Matrices and Sturmian Determinants
Christophe Reutenauer, Jeffrey Shallit
We discuss certain matrices associated with Christoffel words, and show that they have a group structure. We compute their determinants and show a relationship between the Zolotare…
Characterizations of Perfectly Clustering Words
Mélodie Lapointe, Christophe Reutenauer
Perfectly clustering words are one of many possible generalizations of Christoffel words. In this article, we propose a factorization of a perfectly clustering word on a letter…
A Symmetry Property of Christoffel Words
Yan Lanciault, Christophe Reutenauer
Motivated by the theory of trapezoidal words, whose sequences of cardinality of factors by length are symmetric, we introduce a bivariate variant of this symmetry. We show that thi…