Jie Ma

An exponential improvement for the Ramsey lower bounds

For any constant C > 1, let p_C denote the unique solution in (0, 1/2) satisfying C = \log p_C / \log (1 - p_C).We prove a new lower bound on the Ramsey number r(\ell, C\ell) for sufficiently large \ell, showing that there exists \varepsilon(C) > 0 such that r(\ell, C\ell) ≥ (p_C^(-1/2) + \varepsilon(C))^\ell. This provides the first exponential improvement over the classical lower bound by Erdos (1947). Joint work with Wujie Shen (Tsinghua) and Shengjie Xie (USTC).