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arXiv · 1005.0722

On Theta-palindromic Richness

Stepan Starosta
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Abstract

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

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Stepan Starosta. 2010-10-23. On Theta-palindromic Richness. https://doi.org/10.1016/j.tcs.2010.12.011

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