Reinforced Generation of Combinatorial Structures: Ramsey Numbers

ArXi:2603.09172v1 Announce Type: cross We present improved lower bounds for five classical Ramsey numbers: $\mathbf{R}(3, 13)$ is increased from $60$ to $61$, $\mathbf{R}(3, 18)$ from $99$ to $100$, $\mathbf{R}(4, 13)$ from $138$ to $139$, $\mathbf{R}(4, 14)$ from $147$ to $148$, and $\mathbf{R}(4, 15)$ from $158$ to $159$. These results were achieved using~\emph{AlphaEvolve}, an LLM-based code mutation agent. Beyond these new results, we successfully recovered lower bounds for all Ramsey numbers known to be exact, and matched the best known lower bounds across many other cases.