2 01 1 Generalized Thue - Morse words and palindromic richness
نویسنده
چکیده
is valid for any infinite word u with language closed under reversal and for any n. Therefore, the fact that a word u is rich in palindromes expresses that u is saturated by palindromes up to the highest possible level. Arnoux-Rauzy words (among them Sturmian words) and words coding interval exchange transformation with the symmetric permutation belong to the most prominent examples of rich words. Palindrome is a word which coincides with its mirror image, or more formally, w = Θ0(w), where w is a finite word and Θ0 : A 7→ A is defined by Θ0(w1w2 . . . wn) = wnwn−1 . . . w1 for letters wi ∈ A. If we replace the mirror mapping Θ0 by an antimorphism Θ, we can define Θ-palindromes as words which are fixed points of Θ, i.e., w = Θ(w). For any antimorphism Θ, the notion of Θ-palindromic richness can be introduced and
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Languages invariant under more symmetries: Overlapping factors versus palindromic richness
Factor complexity C and palindromic complexity P of infinite words with language closed under reversal are known to be related by the inequality P(n) + P(n + 1) ≤ 2 + C(n + 1) − C(n) for any n ∈ N . Word for which the equality is attained for any n is usually called rich in palindromes. In this article we study words whose languages are invariant under a finite group G of symmetries. For such w...
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