Reinforced Generation of Combinatorial Structures: Ramsey Numbers

arXiv:2603.09172v4 Announce Type: replace-cross Abstract: We present improved lower bounds for seven 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 $148$, $\mathbf{R}(4, 15)$ from $158$ to $159$, $\mathbf{R}(4, 16)$ from $170$ to $174$, and $\mathbf{R}(4, 18)$ from $205$ to $209$. These results were achieved using AlphaEvolve, an LLM-based code mutatio