Palindromic length of infinite aperiodic words

TL;DR

This paper proves the conjecture that the palindromic length of factors in any infinite aperiodic word is unbounded, advancing understanding of the structure of such words.

Contribution

It confirms the 2013 conjecture that the palindromic length of factors in infinite aperiodic words is unbounded, providing a significant theoretical result.

Findings

Confirmed the unboundedness of palindromic length in infinite aperiodic words

Resolved a conjecture posed in 2013

Contributed to the theoretical understanding of word structure

Abstract

The palindromic length of the finite word $v$ is equal to the minimal number of palindromes whose concatenation is equal to $v$. It was conjectured in 2013 that for every infinite aperiodic word $x$, the palindromic length of its factors is not bounded. We prove this conjecture to be true.