Sets of integers with many solutions to a linear equation

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• James Aaronson (University of Oxford)
• Thursday 17 May 2018, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Andrew Thomason.

It is possible to prove, via a fairly elementary argument, that the number of triples x+y=z in a set of integers of given size is maximised for the set [-n/2, n/2]. Suppose we were to consider an equation with arbitrary coefficients; it turns out that we can construct examples of sets which provide a uniform lower bound on the maximal number of solutions. In this talk, we will discuss why such examples are, in some sense, optimal.

This talk is part of the Combinatorics Seminar series.

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