Overlap-free symmetric D0L words.
Applying a uniform marked morphism to a word.
On possible growths of arithmetical complexity
The arithmetical complexity of infinite words, defined by Avgustinovich, Fon-Der-Flaass and the author in 2000, is the number of words of length which occur in the arithmetical subsequences of the infinite word. This is one of the modifications of the classical function of subword complexity, which is equal to the number of factors of the infinite word of length . In this paper, we show that the orders of growth of the arithmetical complexity can behave as many sub-polynomial functions. More precisely,...
On automatic infinite permutations
An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships between these definitions and prove that...
On automatic infinite permutations
An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships...
On automatic infinite permutations
An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships...
Sequences of low arithmetical complexity
Arithmetical complexity of a sequence is the number of words of length that can be extracted from it according to arithmetic progressions. We study uniformly recurrent words of low arithmetical complexity and describe the family of such words having lowest complexity.
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