On z-factorization and c-factorization of standard episturmian words

TL;DR

This paper explores z-factorization and c-factorization of standard episturmian words, extending known results from Sturmian words and comparing the two factorizations to deepen understanding of their structure.

Contribution

It introduces z-factorization for standard episturmian words and compares it with c-factorization, generalizing previous Sturmian word results.

Findings

c-factorization of standard Sturmian words is a special case

z-factorization for standard episturmian words is established

comparison reveals structural differences and similarities

Abstract

Ziv-Lempel and Crochemore factorization are two kinds of factorizations of words related to text processing. In this paper, we find these factorizations for standard epiesturmian words. Thus the previously known c-factorization of standard Sturmian words is provided as a special case. Moreover, the two factorizations are compared.