
TL;DR
This survey explores classical and modern concepts in combinatorics on words, focusing on relations like abelian equivalence and their refinements, providing a unified framework and new insights.
Contribution
It offers a comprehensive overview of combinatorial relations on words, introduces new refinements of abelian equivalence, and unifies various concepts under a common framework.
Findings
Introduction of new refinements of abelian equivalence
Unified framework for combinatorial relations on words
Analysis of Parikh matrices and M-equivalence
Abstract
In the first part of this survey, we present classical notions arising in combinatorics on words: growth function of a language, complexity function of an infinite word, pattern avoidance, periodicity and uniform recurrence. Our presentation tries to set up a unified framework with respect to a given binary relation. In the second part, we mainly focus on abelian equivalence, -abelian equivalence, combinatorial coefficients and associated relations, Parikh matrices and -equivalence. In particular, some new refinements of abelian equivalence are introduced.
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Taxonomy
Topicssemigroups and automata theory · Advanced Combinatorial Mathematics · Coding theory and cryptography
