5 papers
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…
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…