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Geometric structures in pseudo-random graphs

Part of: Finite fields and commutative rings (number-theoretic aspects) Discrete geometry

Published online by Cambridge University Press:  15 March 2024

Thang Pham Open the ORCID record for Thang Pham [Opens in a new window] ,
Steven Senger Open the ORCID record for Steven Senger [Opens in a new window] ,
Michael Tait Open the ORCID record for Michael Tait [Opens in a new window]  and
Vu Thi Huong Thu
Thang Pham*
Affiliation:
University of Science, Vietnam National University, Hanoi, Vietnam
Steven Senger
Affiliation:
Department of Mathematics, Missouri State University, Springfield, MO, United States e-mail: StevenSenger@MissouriState.edu
Michael Tait
Affiliation:
Department of Mathematics and Statistics, Villanova University, Villanova, PA, United States e-mail: michael.tait@villanova.edu
Vu Thi Huong Thu
Affiliation:
University of Science, Vietnam National University, Hanoi, Vietnam e-mail: VuThiHuongThu_T64@hus.edu.vn
*
e-mail: thangpham.math@vnu.edu.vn
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Abstract

In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the continuous setting. The results present interactions between discrete geometry, geometric measure theory, and graph theory.

Keywords

Pseudo-random graphsgeometric structuresfinite fields

MSC classification

Primary: 52C10: Erdős problems and related topics of discrete geometry
Secondary: 11T06: Polynomials

Information

Type
Article
Information
Canadian Journal of Mathematics , Volume 77 , Issue 3 , June 2025 , pp. 1041 - 1071
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

T. Pham was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.99–2021.09. M. Tait was partially supported by National Science Foundation Grant DMS-2011553 and a Villanova University Summer Grant.

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