On Theta-palindromic Richness

Abstract

In this paper we study generalization of the reversal mapping realized by an arbitrary involutory antimorphism $\Theta$. It generalizes the notion of a palindrome into a $\Theta$-palindrome -- a word invariant under $\Theta$. For languages closed under $\Theta$ we give the relation between $\Theta$-palindromic complexity and factor complexity. We generalize the notion of richness to $\Theta$-richness and we prove analogous characterizations of words that are $\Theta$-rich, especially in the case of set of factors invariant under $\Theta$. A criterion for $\Theta$-richness of $\Theta$-episturmian words is given together with other examples of $\Theta$-rich words.

14 pages

References in corpus (4)

• Palindromic Richness
• Episturmian words: a survey
• A connection between palindromic and factor complexity using return words
• A new characteristic property of rich words

Cited by in corpus (7)

• Languages invariant under more symmetries: overlapping factors versus palindromic richness
• Palindromic richness for languages invariant under more symmetries
• Palindromic closures using multiple antimorphisms
• Constructions of words rich in palindromes and pseudopalindromes
• Factor frequencies in languages invariant under more symmetries
• Infinite words rich and almost rich in generalized palindromes
• Generalized Thue-Morse words and palindromic richness