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2019 A family of four-variable expanders with quadratic growth
Mehdi Makhul
Mosc. J. Comb. Number Theory 8(2): 143-149 (2019). DOI: 10.2140/moscow.2019.8.143

Abstract

We prove that if g(x,y) is a polynomial of degree d that is not a polynomial of only y, then for any finite set A

| X | d | A | 2 ,  where  X : = { g ( a 1 , b 1 ) g ( a 2 , b 2 ) b 2 b 1 : a 1 , a 2 , b 1 , b 2 A } .

We will see this bound is also tight for some polynomial g(x,y).

Citation

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Mehdi Makhul. "A family of four-variable expanders with quadratic growth." Mosc. J. Comb. Number Theory 8 (2) 143 - 149, 2019. https://doi.org/10.2140/moscow.2019.8.143

Information

Received: 11 May 2018; Revised: 17 July 2018; Accepted: 31 July 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07063271
MathSciNet: MR3959882
Digital Object Identifier: 10.2140/moscow.2019.8.143

Subjects:
Primary: 11B30
Secondary: 11B75

Rights: Copyright © 2019 Mathematical Sciences Publishers

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