59 research outputs found
Binary words containing infinitely many overlaps
We characterize the squares occurring in infinite overlap-free binary words
and construct various alpha power-free binary words containing infinitely many
overlaps.Comment: 9 page
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
FACTOR AND PALINDROMIC COMPLEXITY OF THUE-MORSE’S AVATARS
Two infinite words that are connected with some significant univoque numbers are studied. It is shown that their factor and palindromic complexities almost coincide with the factor and palindromic complexities of the famous Thue-Morse word
Words with the Maximum Number of Abelian Squares
An abelian square is the concatenation of two words that are anagrams of one
another. A word of length can contain distinct factors that
are abelian squares. We study infinite words such that the number of abelian
square factors of length grows quadratically with .Comment: To appear in the proceedings of WORDS 201
A relative of the Thue-Morse sequence
We study a sequence, c, which encodes the lengths of blocks in the Thue-Morse sequence. In particular, we show that the generating function for c is a simple product
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