A note on lower bounds for hypergraph Ramsey numbers

TL;DR

This paper improves the lower bounds for 3-color hypergraph Ramsey numbers, demonstrating a super-exponential growth rate in the 3-uniform case, which advances understanding of combinatorial complexity.

Contribution

It establishes a significantly stronger lower bound for 3-uniform hypergraph Ramsey numbers, surpassing previous results by Erdős and Hajnal.

Findings

Lower bound for r_3(l,l,l) is at least 2^{l^{c log log l}}

Previous bound was 2^{c l^2 log^2 l}

Shows super-exponential growth in hypergraph Ramsey numbers

Abstract

We improve upon the lower bound for 3-colour hypergraph Ramsey numbers, showing, in the 3-uniform case, that \[r_3 (l,l,l) \geq 2^{l^{c \log \log l}}.\] The old bound, due to Erd\H{o}s and Hajnal, was \[r_3 (l,l,l) \geq 2^{c l^2 \log^2 l}.\]