Proves f_{F,G}(n) ≤ C (log n)^{β_F} for r-uniform hypergraphs under the stated conditions on F and G, sharpening prior bounds and confirming a conjecture for r=3.
Off-diagonal Ramsey numbers
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
For positive integers $s$ and $k$, the Ramsey number $r(s,k)$ is the minimum integer $n$ such that any graph on $n$ vertices contains a clique of size $s$ or an independent set of size $k$. We prove that for any fixed $s \ge 3$ and $k$ tending to infinity, the off-diagonal Ramsey numbers satisfy \[ r(s, k) \ge \Omega \left(\frac{k^{s-1}}{(\log k)^{2s-4}} \right), \] which matches, up to polylogarithmic factors, the upper bound established over 90 years ago by Erd\H{o}s and Szekeres. For $s \ge 5,$ this improves the best known lower bound of the form $r(s, k) \ge k^{\frac{s+1}{2} + o(1)}$ which was first established by Spencer in 1977 and has since only seen polylogarithmic improvements.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
Improves r_k(k+1,k+1) > s_3(⌊k/2⌋-2) for k≥6 and proves s_3(k) ≥ (twr_{k-2}(2))^2 for k≥5, yielding r_k(k+1,k+1) > (twr_{⌊k/2⌋-4}(2))^2 for k≥14.
Trellis applies process semantics to guide generalist LLM agents through incremental refinement of proofs for reliable Lean autoformalization, shown via a Ramsey theory example.
citing papers explorer
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Generalized Erd\H{o}s--Rogers problems for $r$-uniform hypergraphs
Proves f_{F,G}(n) ≤ C (log n)^{β_F} for r-uniform hypergraphs under the stated conditions on F and G, sharpening prior bounds and confirming a conjecture for r=3.
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New Tower-Type Lower Bounds for Hypergraph Ramsey Numbers
Improves r_k(k+1,k+1) > s_3(⌊k/2⌋-2) for k≥6 and proves s_3(k) ≥ (twr_{k-2}(2))^2 for k≥5, yielding r_k(k+1,k+1) > (twr_{⌊k/2⌋-4}(2))^2 for k≥14.
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(Auto)formalization is supposed to be easy: Trellis process semantics for spelling out rigorous proofs
Trellis applies process semantics to guide generalist LLM agents through incremental refinement of proofs for reliable Lean autoformalization, shown via a Ramsey theory example.