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Short proofs in combinatorics, probability and number theory II

2 Pith papers cite this work. Polarity classification is still indexing.

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abstract

We give a quintet of proofs resulting from questions posed by Erd\H{o}s. 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 Erd\H{o}s--Tur\'{a}n discrepancy bound, and a finiteness theorem for integers $n$ such that $n-a k^2$ is prime for all $k\leq \sqrt{n/a}$ coprime to $n$ (for fixed $a\in\mathbb Z_+$). Each proof is due to an internal model at OpenAI.

fields

cs.AI 1 cs.CL 1

years

2026 2

verdicts

UNVERDICTED 2

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