<abstract xmlns="http://www.w3.org/1999/xhtml">

In this note we give an overview of the currently known best lower and upper bounds on the size of a subset of ℤ<italic>nm</italic> avoiding <italic>k</italic>-term arithmetic progression. We will focus on the case when the length of the forbidden progression is 3. We also formulate some open questions.
</abstract>

In this note we give an overview of the currently known best lower and upper bounds on the size of a subset of ℤnm avoiding k-term arithmetic progression. We will focus on the case when the length of the forbidden progression is 3. We also formulate some open questions.

Bounds on the size of Progression-Free Sets in ℤ<italic>mn</italic>

Department of Computer Science and Information Theory

Budapest University of Technology and Economics

Uniform distribution theory

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

Bounds on the size of Progression-Free Sets in ℤ

In this note we give an overview of the currently known best lower and upper bounds on the size of a subset of ℤnm avoiding k-term arithmetic progression. We...

Bounds on the size of Progression-Free Sets in ℤ_mⁿ

Publié en ligne: 31 mai 2022

Pages: 1 - 10

Reçu: 30 juin 2021

Accepté: 18 nov. 2021

DOI: https://doi.org/10.2478/udt-2022-0005

Mots clés
progression-free sets, cap set problem, polynomial method

© 2022 Péter Pál Pach, published by Sciendo

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

Bounds on the size of Progression-Free Sets in ℤmn

Publié en ligne: 31 mai 2022

Pages: 1 - 10

Reçu: 30 juin 2021

Accepté: 18 nov. 2021

DOI: https://doi.org/10.2478/udt-2022-0005

Mots clésprogression-free sets, cap set problem, polynomial method

© 2022 Péter Pál Pach, published by Sciendo

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

Bounds on the size of Progression-Free Sets in ℤ_mⁿ

Mots clés
progression-free sets, cap set problem, polynomial method