On Theta-palindromic Richness

Details On Theta-palindromic Richness On Theta-palindromic Richness

2010-05-05

arxiv.org/abs/1005.0722v2

Mathematics

Combinatorics

14 pages

Scientific paper

10.1016/j.tcs.2010.12.011

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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