On maximal chains of systems of word equations

TL;DR

This paper explores the properties of systems of word equations, focusing on the size of maximal independent sets and chains of solution sets, extending known results and proposing fundamental open problems.

Contribution

It extends existing results on word equations and introduces new fundamental problems related to chains and independence in solution sets.

Findings

Analysis of maximal independent sets of word equations

Extension of known results in the theory of word equations

Formulation of fundamental open problems in the field

Abstract

We consider systems of word equations and their solution sets. We discuss some fascinating properties of those, namely the size of a maximal independent set of word equations, and proper chains of solution sets of those. We recall the basic results, extend some known results and formulate several fundamental problems of the topic.