Computations for symbolic substitutions

Abstract

We provide a survey of results from symbolic dynamics and algebraic topology relating to Grout, a new user-friendly program developed to calculate combinatorial properties and topological invariants of a large class of symbolic substitutions. We study their subshifts (and related spaces) with an emphasis on examples of computations. We implement a check to verify that no counterexample exists to the so-called "strong coincidence conjecture" for a large number of substitutions on three and four letters.