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Substitutions in dynamics, arithmetics, and combinatorics
Basic notions on substitutions.- Basic notions on substitutions.- Arithmetics and combinatorics of substitutions.- Substitutions, arithmetic and finite automata: an introduction.- Automatic sequencesExpand
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On Finite Pseudorandom Binary Sequences
Special finite binary sequences are tested for pseudorandomness. As measures of pseudorandomness, well-distribution relative to arithmetic progressions and small (auto)correlation are used. TheseExpand
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On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol
On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol by Christian Mauduit (Marseille) and András Sárközy (Budapest) 1. Introduction. In the last 60 yearsExpand
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Transcendence of Numbers with a Low Complexity Expansion
Abstract A sequence is Sturmian if it has complexity n + l −1, that is, n + l −1 factors of length n for every n ; we show that real numbers whose expansion in some base k ⩾ l is Sturmian areExpand
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On finite pseudorandom binary sequences VII: The measures of pseudorandomness
where the maximum is taken over all D = (d1, . . . , dk) and M such that M + dk ≤ N . 2000 Mathematics Subject Classification: Primary 11K45.
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A complexity measure for families of binary sequences
It is shown that the family of “good” pseudorandom binary sequences constructed earlier is also of high f-complexity. Expand
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Prime numbers along Rudin–Shapiro sequences
For a large class of digital functions f, we estimate the sums Sigma(n <= x) Lambda(n)f (n) (and Sigma(n <= x) mu(n)f (n)), where Lambda denotes the von Mangoldt function (and mu, the MobiusExpand
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Construction of large families of pseudorandom binary sequences
Abstract In a series of papers Mauduit and Sarkozy (partly with coauthors) studied finite pseudorandom binary sequences. They showed that the Legendre symbol forms a “good” pseudorandom sequence, andExpand
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Measures of pseudorandomness for finite sequences: typical values
Mauduit and Sárközy introduced and studied certain numerical parameters associated to finite binary sequences EN ∈ {−1, 1}N in order to measure their ‘level of randomness’. Those parameters, theExpand
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