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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 17. Issue 1


Published on

June, 2022


Pages

1-10


DOI

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

Article

Bounds on the size of Progression-Free Sets in ℤmn


Authors

Péter Pál Pach


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.


Citation

Pach, P.P. (2022). Bounds on the size of Progression-Free Sets in ℤmn. Uniform distribution theory, 17(1), 1-10. https://doi.org/10.2478/udt-2022-0005