Uniformly balanced words with linear complexity and prescribed letter frequencies

We consider the following problem. Let us fix a finite alphabet A; for any given d-uple of letter frequencies, how to construct an infinite word u over the alphabet A satisfying the following conditions: u has linear complexity function, u is uniformly balanced, the letter frequencies in u are given by the given d-uple. This paper investigates a construction method for such words based on the use of mixed multidimensional continued fraction algorithms.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Characterization of the Closest Discrete Approximation of a Line in the 3-Dimensional Space

International audienceThe present paper deals with discrete lines in the $3$-dimensional space. In particular, we focus on the minimal $0$-connected set of closest integer points to a Euclidean line. We propose a definition which leads to geometric, arithmetic and algorithmic characterizations of naive discrete lines in the $3$-dimensional space