On the fixed point of the iterated pseudopalindromic closure

TL;DR

This paper explores the combinatorial properties of fixed points generated by the iterated pseudopalindromic closure, a generalization of palindromic closure, revealing new insights into pseudostandard words.

Contribution

It provides new combinatorial insights into the fixed points of the iterated pseudopalindromic closure, extending previous work on palindromic structures.

Findings

Characterization of fixed points under the iterated pseudopalindromic closure

Properties of pseudostandard words with infinite pseudopalindromic prefixes

Extension of classical palindromic closure results to pseudopalindromes

Abstract

First introduced in the study of the Sturmian words, the iterated palindromic closure was recently generalized to pseudopalindromes. This operator allows one to construct words with an infinity of pseudopalindromic prefixes, called pseudostandard words. We provide here several combinatorial properties of the fixed points under the iterated pseudopalindromic closure.