- Détails du magazine
- Format
- Magazine
- eISSN
- 2309-5377
- Première publication
- 30 Dec 2013
- Période de publication
- 2 fois par an
- Langues
- Anglais

#### Chercher

- Accès libre

A curiosity About (− 1)^{[}^{e}^{]} +(− 1)^{[2}^{e}^{]} + ··· +(− 1)^{[}^{Ne}^{]}

^{[}

^{e}

^{]}+(

^{[2}

^{e}

^{]}+

^{[}

^{Ne}

^{]}

Pages: 1 - 8

#### Résumé

Let _{N}^{[}^{α}^{]} +(^{[2}^{α}^{]} + ^{[}^{Nα}^{]} depends on the continued fraction expansion of

#### Mots clés

- Oscillating sums
- uniform distribution modulo 1

#### MSC 2010

- Primary 11K38
- Secondary 11A55

- Accès libre

On the Maximum Order Complexity of Thue–Morse and Rudin–Shapiro Sequences along Polynomial Values

Pages: 9 - 22

#### Résumé

Both the Thue–Morse and Rudin–Shapiro sequences are not suitable sequences for cryptography since their expansion complexity is small and their correlation measure of order 2 is large. These facts imply that these sequences are highly predictable despite the fact that they have a large maximum order complexity. Sun and Winterhof (2019) showed that the Thue–Morse sequence along squares keeps a large maximum order complexity. Since, by Christol’s theorem, the expansion complexity of this rarefied sequence is no longer bounded, this provides a potentially better candidate for cryptographic applications. Similar results are known for the Rudin–Shapiro sequence and more general pattern sequences. In this paper we generalize these results to any polynomial subsequence (instead of squares) and thereby answer an open problem of Sun and Winterhof. We conclude this paper by some open problems.

#### Mots clés

- Automatic sequences
- pseudorandomness
- Thue–Morse sequence
- Rudin–Shapiro sequence
- polynomials

#### MSC 2010

- 11A63
- 11B85

- Accès libre

Word Metric, Stationary Measure and Minkowski’s Question Mark Function

Pages: 23 - 38

#### Résumé

Given a countably infinite group _{n}_{n}_{g∈Gn}f_{n}_{n}^{∗n}

#### Mots clés

- Stationary measure
- Minkowski’s question matk function
- Word metric
- Lattice orbits

#### MSC 2010

- 22E40
- 30B70
- 60G10

#### Résumé

In 1986, Proinov published an explicit lower bound for the diaphony of finite and infinite sequences of points contained in the _{2}_{2}_{2}

#### Mots clés

- ℒ-discrepancy
- (dyadic) diaphony
- Walsh system
- Haar system

#### MSC 2010

- 11K38

- Accès libre

The Distribution of Rational Numbers on Cantor’s Middle Thirds Set

Pages: 73 - 92

#### Résumé

We give a heuristic argument predicting that the number ^{∗}^{d}^{+}^{ε}^{∗}

#### Mots clés

- Rational numbers in the Cantor set

#### MSC 2010

- 11K60: Diophantine approximation in probabilistic number theory

- Accès libre

Point Distribution and Perfect Directions in ${\mathbb{F}}_{p}^{2}$\mathbb{F}_p^2

Pages: 93 - 98

#### Résumé

Let

As an application, we give a new proof of a result of Rédei-Megyesi about the number of directions determined by a set in a finite affine plane.

#### Mots clés

- Uniform distribution
- affine plane

#### MSC 2010

- Primary: 05B25
- Secondary: 51E99

- Accès libre

On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

Pages: 99 - 112

#### Résumé

Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type
_{C}^{2} of a specific type. Such problems have been considered in [4] and are of interest in the study of limit points of two uniformly distributed sequences.

#### Mots clés

- Uniform distribution
- Copulas
- Extremal problems

#### MSC 2010

- 11K06
- 62H05