Describing the set of words generated by interval exchange transformation

TL;DR

This paper provides combinatorial criteria to determine when an infinite word over a finite alphabet can be generated by an interval exchange transformation, linking combinatorics and dynamical systems.

Contribution

It introduces new combinatorial criteria for identifying words generated by interval exchange transformations, advancing understanding of their structure.

Findings

Established criteria for the existence of interval exchange transformations generating a given word.

Connected combinatorial properties of words with dynamical systems theory.

Provided a framework for analyzing infinite words via interval exchange transformations.

Abstract

Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.