Infinite permutations of lowest maximal pattern complexity
نویسندگان
چکیده
منابع مشابه
Low maximal pattern complexity of infinite permutations
An infinite permutation α is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words and showing some resemblance and some difference between permutations and words. In this paper, we define maximal pattern complexity pα(n) for infinite permutations and show that this complexity function is ultimately constant if and only if the permutation is u...
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An infinite permutation can be defined as a linear ordering of the set of natural numbers. Similarly to infinite words, a complexity p(n) of an infinite permutation is defined as a function counting the number of its factors of length n. For infinite words, a classical result of Morse and Hedlind, 1940, states that if the complexity of an infinite word satisfies p(n) ≤ n for some n, then the wo...
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In the paper we investigate a new natural notion of ergodic infinite permutations, that is, infinite permutations which can be defined by equidistributed sequences. We show that, unlike for permutations in general, the minimal complexity of an ergodic permutation α is pα(n) = n. The class of ergodic permutations of minimal complexity coincides with the class of so-called Sturmian permutations, ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2011
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2010.12.062