Multidimensional Sturmian Sequences and Generalized Substitutions
Abstract
This paper is devoted to a study on the way \emph{generalized substitutions} - a multi-dimensional extension of substitutions - act on \emph{multi-dimensional Sturmian sequences}. We give a sufficient condition under which these multi-dimensional Sturmian sequences are obtained by iterated compositions of generalized substitutions. This condition relies on Brun expansions - a multi-dimensional extension of continued fraction expansions.