Perfectly Clustering Words and Iterated Palindromes over a Ternary Alphabet

TL;DR

This paper explores the properties of perfectly clustering Lyndon words over a ternary alphabet, focusing on their structure as products of palindromes and their relation to iterated palindromes.

Contribution

It introduces a new characterization of perfectly clustering Lyndon words over a ternary alphabet and investigates the properties of their palindrome factors.

Findings

Characterization of perfectly clustering Lyndon words as products of two palindromes

Analysis of the structure of palindrome factors p and q

Connections between these words and iterated palindromes

Abstract

Recently, a new characterization of Lyndon words that are also perfectly clustering was proposed by Lapointe and Reutenauer (2024). A word over a ternary alphabet {a,b,c} is called perfectly clustering Lyndon if and only if it is the product of two palindromes and it can be written as apbqc where p and q are palindromes. We study the properties of palindromes appearing as factors p and q and their links with iterated palindromes over a ternary alphabet.