Decomposition theorem for invertible substitutions on three - letter alphabet ∗

Invertible Substitutions with a Common Periodic Point

We characterize the invertible substitutions over a two-letter alphabet which share a common periodic point (or fixed point). The argument is geometrical.

A Class of Two Generated Automaton Groups on a Three Letter Alphabet

On substitution invariant Sturmian words: an application of Rauzy fractals

Sturmian words are infinite words that have exactly n+ 1 factors of length n for every positive integer n. A Sturmian word sα,ρ is also defined as a coding over a two-letter alphabet of the orbit of point ρ under the action of the irrational rotation Rα : x 7→ x+ α (mod 1). A substitution fixes a Sturmian word if and only if it is invertible. The main object of the present paper is to investiga...

The effects of teaching English alphabet with and without initial introduction of letter names on Iranian grade seven students' reading speed

One of the most important steps in teaching English is teaching its alphabet to the learners. Implementing the best method will highly help teachers to achieve acceptable results in helping students to read better and faster. Two basic methods are frequently used by Iranian educators. Some start by the name of the letters and introduce the sounds that they symbolize later, while others are thos...

On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata

This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers with the same input and output alphabet. The torsion problem is undecidable for automaton semigroups in general, but is known to be solvable within the well-studied class of (semi)groups generated by invertible bounded...