<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In Part I of this paper we studied the irregularities of distribution of binary sequences relative to short arithmetic progressions. First we introduced a quantitative measure for this property. Then we studied the typical and minimal values of this measure for binary sequences of a given length. In this paper our goal is to give constructive bounds for these minimal values.</p></abstract>

In Part I of this paper we studied the irregularities of distribution of binary sequences relative to short arithmetic progressions. First we introduced a quantitative measure for this property. Then we studied the typical and minimal values of this measure for binary sequences of a given length. In this paper our goal is to give constructive bounds for these minimal values.

On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, II (Constructive Bounds)

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In Part I of this paper we studied the irregularities of distribution of binary sequences relative to short arithmetic progressions. First we introduced a...

On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, II (Constructive Bounds)

Published Online: Jan 25, 2019

Page range: 1 - 21

Received: Dec 20, 2016

Accepted: Nov 11, 2017

DOI: https://doi.org/10.2478/udt-2018-0008

Keywords
arithmetic progressions, irregularities of distribution, binary sequences

© 2018 Cécile Dartyge et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, II (Constructive Bounds)

Published Online: Jan 25, 2019

Page range: 1 - 21

Received: Dec 20, 2016

Accepted: Nov 11, 2017

DOI: https://doi.org/10.2478/udt-2018-0008

Keywordsarithmetic progressions, irregularities of distribution, binary sequences

© 2018 Cécile Dartyge et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
arithmetic progressions, irregularities of distribution, binary sequences