Palindromic length of words and morphisms in class $\mathcal{P}$
Petr Ambro\v{z}, Ond\v{r}ej Kadlec, Zuzana Mas\'akov\'a, Edita, Pelantov\'a

TL;DR
This paper investigates how the palindromic length of factors in infinite words fixed by class P morphisms grows, showing logarithmic bounds and providing specific estimates for Fibonacci and Thue-Morse words.
Contribution
It establishes growth bounds for palindromic length in class P morphic words and constructs a new example with different growth behavior.
Findings
Palindromic length grows at most logarithmically for class P morphic words.
Specific growth constants are estimated for Fibonacci and Thue-Morse words.
A new infinite word with palindromic length growing as √n is constructed.
Abstract
We study the palindromic length of factors of infinite words fixed by morphisms of the so-called class introduced by Hof, Knill and Simon. We show that it grows at most logarithmically with the length of the factor. For the Fibonacci word and the Thue-Morse word we provide estimates on the constants of the growth. We also construct an infinite word rich in palindromes for which the palindromic length grows as .
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · Geometric and Algebraic Topology
