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.
An update on multicolor Ramsey lower bounds
2 Pith papers cite this work. Polarity classification is still indexing.
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The vertex-coloring coprime Ramsey number R_cop(k1,...,kc) equals the prime p indexed by sum(ki-1).
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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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Prime Certificates for Exact Vertex-Coprime Ramsey Numbers
The vertex-coloring coprime Ramsey number R_cop(k1,...,kc) equals the prime p indexed by sum(ki-1).