Bounds on the size of Progression-Free Sets in ℤmn

Péter Pál Pach

doi:10.2478/udt-2022-0005

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Bounds on the size of Progression-Free Sets in ℤmn

Uniform distribution theory

Volume 17 (2022): Issue 1 (May 2022)

By: Péter Pál Pach

Open Access

|May 2022

Abstract

In this note we give an overview of the currently known best lower and upper bounds on the size of a subset of ℤⁿ_m 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.

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Articles in this issue

DOI: https://doi.org/10.2478/udt-2022-0005 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 1 - 10

Submitted on: Jun 30, 2021

Accepted on: Nov 18, 2021

Published on: May 31, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

progression-free sets,

cap set problem,

polynomial method

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2022 Péter Pál Pach, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 17 (2022): Issue 1 (May 2022)