Short proofs in combinatorics, probability and number theory II

by Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, and Gregory Valiant

Abstract

We give a quintet of proofs resulting from questions posed by Erdős. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums, \(K_4\)-free \(4\)-critical graphs with few chords in any cycle, a counterexample to a "fewnomial" version of the Erdős--Turán discrepancy bound, and a finiteness theorem for integers \(n\) such that \(n-ak^2\) is prime for all \(k \le \sqrt{n/a}\) coprime to \(n\) (for fixed \(a\in\mathbb{Z}_+\)). Each proof is due to an internal model at OpenAI.

Approximate citation

Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, and Gregory Valiant
Short proofs in combinatorics, probability and number theory II

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