Palindromic richness for languages invariant under more symmetries

Abstract

For a given finite group $G$ consisting of morphisms and antimorphisms of a free monoid ${\mathcal{A}}^{\ast }$, we study infinite words with language closed under the group $G$. We focus on the notion of $G$-richness which describes words rich in generalized palindromic factors, i.e., in factors $w$ satisfying $\Theta (w)=w$ for some antimorphism $\Theta \in G$. We give several equivalent descriptions which are generalizations of know characterizations of rich words (in the terms of classical palindromes) and show two examples of $G$-rich words.

References in corpus (4)

• Languages invariant under more symmetries: overlapping factors versus palindromic richness
• Bispecial factors in circular non-pushy D0L languages
• Proof of Brlek-Reutenauer conjecture
• Factor frequencies in languages invariant under more symmetries

Cited by in corpus (6)

• Acyclic, connected and tree sets
• Languages invariant under more symmetries: overlapping factors versus palindromic richness
• On Number of Rich Words
• Constructions of words rich in palindromes and pseudopalindromes
• Morphic images of episturmian words having finite palindromic defect
• On Words with the Zero Palindromic Defect