Researchers have utilized an LLM-enhanced evolutionary algorithm called OpenEvolve to discover new bounds for Zarankiewicz numbers, which relate to the maximum edges in bipartite graphs without specific complete subgraphs. This approach successfully determined exact values for three Zarankiewicz numbers and established lower bounds for 41 others, including several close to existing upper bounds. The method proved to be cost-effective, with computations costing less than $30 per parameter combination, showcasing LLM-guided evolutionary search as an accessible tool for mathematical discovery. AI
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IMPACT Demonstrates LLM-guided evolutionary search as a cost-effective tool for advancing mathematical research and combinatorial discovery.
RANK_REASON Academic paper detailing a new method for mathematical discovery using LLM-guided evolutionary search. [lever_c_demoted from research: ic=1 ai=1.0]