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Generalized Thue-Morse words and palindromic richness
We prove that the generalized Thue-Morse word defined for
and as , where denotes the sum of digits in the base-
representation of the integer , has its language closed under all elements
of a group isomorphic to the dihedral group of order consisting of
morphisms and antimorphisms. Considering simultaneously antimorphisms , we show that is saturated by -palindromes
up to the highest possible level. Using the terminology generalizing the notion
of palindromic richness for more antimorphisms recently introduced by the
author and E. Pelantov\'a, we show that is -rich. We
also calculate the factor complexity of .Comment: 11 page
Complexity of testing morphic primitivity
We analyze the algorithm in [Holub, 2009], which decides whether a given word
is a fixed point of a nontrivial morphism. We show that it can be implemented
to have complexity in O(mn), where n is the length of the word and m the size
of the alphabet
Equation in words
We will prove that the word is periodicity forcing if
and , where and are positive integers. Also we will give
examples showing that both bounds are optimal
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