Proves r(s, k) ≥ Ω(k^{s-1} / (log k)^{2s-4}) for fixed s ≥ 3 and k → ∞, nearly matching the Erdős-Szekeres upper bound and improving the Spencer lower bound for s ≥ 5.
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11 Pith papers cite this work. Polarity classification is still indexing.
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Uncrouded k-uniform hypergraphs attain independence number (1-ε)n ((log Δ)/((k-1)Δ))^{1/(k-1)} for large Δ, matching the shattering threshold.
r_4(5,n) is at least 2^{2^{c n^{1/7}}}, determining the tower growth rate of r_k(k+1,n) 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.
f^{(4)}_{5^{-},6}(N) equals (log log N) to the Theta(1) power, with improved lower bounds r_4(6,n) >= 2^{2^{c sqrt(n)}} and r_k(k+2,n).
Zero-sum Ramsey numbers R(G, Γ) satisfy R(G, Γ) ≤ C n for bounded-degree n-vertex graphs G whenever |Γ| divides e(G).
For every fixed odd ℓ > 7 the Ramsey number satisfies r(C_ℓ, K_k) ≥ k^{1 + 1/(ℓ-2) + ε_ℓ + o(1)} as k tends to infinity, for some positive ε_ℓ depending only on ℓ.
Simplified proof of exponential Ramsey lower bound improvements via Gaussian random graphs, with better quantitative constants than prior work.
Trellis applies process semantics to guide generalist LLM agents through incremental refinement of proofs for reliable Lean autoformalization, shown via a Ramsey theory example.
The exponent in the lower bound for R(ℓ, Cℓ) increases by a positive amount for every fixed C>1, with asymptotic gain Θ(p_C^{-1/2}/log C) as C grows.
The paper establishes the improved lower bound r_4(5,n) >= 2^{2^{Omega(n^{1/5})}} for the 4-uniform 5-clique Ramsey number by reducing greedy local-maxima selection from seven layers to five in a modified construction.
citing papers explorer
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Off-diagonal Ramsey numbers
Proves r(s, k) ≥ Ω(k^{s-1} / (log k)^{2s-4}) for fixed s ≥ 3 and k → ∞, nearly matching the Erdős-Szekeres upper bound and improving the Spencer lower bound for s ≥ 5.
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The independence number of uncrowded hypergraphs: bounds matching the shattering threshold
Uncrouded k-uniform hypergraphs attain independence number (1-ε)n ((log Δ)/((k-1)Δ))^{1/(k-1)} for large Δ, matching the shattering threshold.
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A double-exponential lower bound for $r_4(5,n)$
r_4(5,n) is at least 2^{2^{c n^{1/7}}}, determining the tower growth rate of r_k(k+1,n) for hypergraph Ramsey numbers.
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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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A Note on Generalized Erd\H{o}s-Rogers Problems
f^{(4)}_{5^{-},6}(N) equals (log log N) to the Theta(1) power, with improved lower bounds r_4(6,n) >= 2^{2^{c sqrt(n)}} and r_k(k+2,n).
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A linear upper bound for zero-sum Ramsey numbers of bounded degree graphs
Zero-sum Ramsey numbers R(G, Γ) satisfy R(G, Γ) ≤ C n for bounded-degree n-vertex graphs G whenever |Γ| divides e(G).
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A polynomial improvement for the odd cycle-complete Ramsey numbers
For every fixed odd ℓ > 7 the Ramsey number satisfies r(C_ℓ, K_k) ≥ k^{1 + 1/(ℓ-2) + ε_ℓ + o(1)} as k tends to infinity, for some positive ε_ℓ depending only on ℓ.
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Gaussian random graphs and Ramsey numbers
Simplified proof of exponential Ramsey lower bound improvements via Gaussian random graphs, with better quantitative constants than prior work.
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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.
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Sharper Ramsey lower bounds from refined Gaussian estimates
The exponent in the lower bound for R(ℓ, Cℓ) increases by a positive amount for every fixed C>1, with asymptotic gain Θ(p_C^{-1/2}/log C) as C grows.
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An improved double-exponential lower bound for $r_4(5,n)$
The paper establishes the improved lower bound r_4(5,n) >= 2^{2^{Omega(n^{1/5})}} for the 4-uniform 5-clique Ramsey number by reducing greedy local-maxima selection from seven layers to five in a modified construction.