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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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).
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.
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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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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.