Expanders on matrices over a finite chain ring, I-Reference-Cited by-同舟云学术

Expanders on matrices over a finite chain ring, I

Published:2023-05-15 Issue:07 Volume:34 Page:
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Ha Dung M.¹,Ngo Hieu T.²^ORCID

Affiliation:

1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

2. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

Abstract

In this work and its sequel, we study the expanding phenomenon of matrices over a finite chain ring of large residue field. A sum-product estimate is proved. It is shown that [Formula: see text] is a moderate expander on [Formula: see text] matrices with exponent [Formula: see text]. These results generalize the main theorems in the recent work [29] of Xie and Ge. The proofs use spectral graph theory and elementary divisor theory.

Funder

Vietnam Academy of Science and Technology

Qui mi sng to Vingroup

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X23500349

Reference29 articles.

1. Group actions and geometric combinatorics in 𝔽 q d $\mathbb{F}_{q}^{d}$

2. A sum-product estimate in finite fields, and applications

3. Monographs and Textbooks in Pure and Applied Mathematics;Brown W. C.,1993

4. Additive and Multiplicative Structure in Matrix Spaces

5. Moderate expanders over rings

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