Normal basises and symbolical dynamics

TL;DR

This paper explores the connections between algebra and symbolic dynamics, providing criteria for when infinite words can be generated by interval exchange transformations without restrictive assumptions.

Contribution

It offers a comprehensive set of combinatorial criteria for the existence of interval exchange transformations generating given infinite words, including non-orientation-preserving cases.

Findings

Criteria for interval exchange transformations generating infinite words

Generalization of Sturmian sequences

No IDOC condition required

Abstract

The thesis is devoted to relations between algebra and symbolic dynamics. Various generalisations of sturmian sequences are discoursed. Let $W$ be an infinite word over a finite alphabet $A$. The combinatorial criteria of existence of interval exchange transformations that generate the word $W$ is obtained in full generality -- no IDOC condition assumed, case of orientation non-preserving also considered.