Palindromic closures using multiple antimorphisms

Abstract

Generalized pseudostandard word $\mathbf{u}$, as introduced in 2006 by de Luca and De Luca, is given by a directive sequence of letters from an alphabet $\mathcal{A}$ and by a directive sequence of involutory antimorphisms acting on ${\mathcal{A}}^{\ast }$. Prefixes of $\mathbf{u}$ with increasing length are constructed using pseudopalindromic closure operator. We show that generalized Thue--Morse words ${\mathbf{t}}_{b,m}$, with $b,m\in \mathbb{N}$ and $b,m\ge 2$, are generalized pseudostandard words if and only if ${\mathbf{t}}_{b,m}$ is a periodic word or $b\le m$. This extends the result of de Luca and De Luca obtained for the classical Thue--Morse words.

16 pages

Cited by in corpus (4)

• Constructions of words rich in palindromes and pseudopalindromes
• On Words with the Zero Palindromic Defect
• A new estimate on complexity of binary generalized pseudostandard words
• On Periodicity and Complexity of Generalized Pseudostandard Words