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On Theta-palindromic Richness

Authors
  • Starosta, Stepan
Type
Published Article
Publication Date
Oct 23, 2010
Submission Date
May 05, 2010
Identifiers
DOI: 10.1016/j.tcs.2010.12.011
Source
arXiv
License
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External links

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.

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