Vol. 8, No. 2, 2019

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A family of four-variable expanders with quadratic growth

Mehdi Makhul

Vol. 8 (2019), No. 2, 143–149

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(a1,b1) g(a2,b2) b2 b1 : a1,a2,b1,b2 A}.

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

Bisector, expander functions
Mathematical Subject Classification 2010
Primary: 11B30
Secondary: 11B75
Received: 11 May 2018
Revised: 17 July 2018
Accepted: 31 July 2018
Published: 20 May 2019
Mehdi Makhul
Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Austrian Academy of Sciences, Linz and Research Institute for Symbolic Computation (RISC)
Johannes Kepler University