<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

Online veröffentlicht: 31. Mai 2022

Seitenbereich: 1 - 10

Eingereicht: 30. Juni 2021

Akzeptiert: 18. Nov. 2021

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

Schlüsselwörter
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

Online veröffentlicht: 31. Mai 2022

Seitenbereich: 1 - 10

Eingereicht: 30. Juni 2021

Akzeptiert: 18. Nov. 2021

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

Schlüsselwörterprogression-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

Schlüsselwörter
progression-free sets, cap set problem, polynomial method