Multidimensional continued fractions, numeration and discrete geometry

Valérie Berthé

LIRM, CNRS, Montpellier, France

Coauthor(s): Thomas Fernique

The aim of this lecture is to discuss a discrete plane recognition algorithm connected with Brun's continued fraction algorithm. The problem of the discrete plane recognition consists in deciding whether a given set of points with integer coordinates can be described as a plane discretization. We will first give a geometric interpretation of Brun's continued fraction algorithm in terms of the so-called generalized substitutions introduced by Arnoux and Ito. We will then focus on a multidimensional version of Ostrowski's numeration.