Researchers improve lower bounds for some Ramsey numbers using AlphaEvolve
a day ago
- #Ramsey Theory
- #Combinatorics
- #Lower Bounds
- Improved lower bounds for five classical Ramsey numbers using AlphaEvolve, an LLM-based code mutation agent.
- Increased R(3,13) from 60 to 61, R(3,18) from 99 to 100, R(4,13) from 138 to 139, R(4,14) from 147 to 148, and R(4,15) from 158 to 159.
- Recovered lower bounds for all Ramsey numbers known to be exact and matched best known lower bounds across many other cases.
- AlphaEvolve serves as a single meta-algorithm yielding search algorithms for all results, unlike previous bespoke search algorithms.