Description
We are considering a problem posted by Imre Ruzsa in the early 90's. Consider the linear form L(x,y,z,w) = 3x + y - 2z-2w. For a positive integer N, let r_L(N) denote the largest size of a subset of {1,2,..., N} that avoids nontrivial solutions to L = 0. We show that r_L(N) > N^{0.56}, improving the previous lower bound N^{1/2}.
Our method also works for different linear forms.
Joint work with Paul Hametner
október 20-a, 14:15, Rényi Intézet, Nagyterem (Main Lecture Hall)
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