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LLMs and SAT solvers aid mathematicians in discovering infinite graph families

Researchers have developed a novel method combining SAT solvers with LLM-generated code to discover infinite families of doubly saturated Ramsey-good graphs. This approach successfully answers a question posed by Grinstead and Roberts in 1982. Furthermore, the study utilized LLMs to generate and formalize proofs of correctness in Lean, demonstrating the potential of integrating automated reasoning, LLMs, and formal verification for advancing mathematical discovery. AI

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RANK_REASON This is a research paper detailing a novel method for mathematical discovery using AI tools.

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LLMs and SAT solvers aid mathematicians in discovering infinite graph families

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  1. Hugging Face Daily Papers TIER_1 ·

    Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery

    Ramsey-good graphs are graphs that contain neither a clique of size $s$ nor an independent set of size $t$. We study doubly saturated Ramsey-good graphs, defined as Ramsey-good graphs in which the addition or removal of any edge necessarily creates an $s$-clique or a $t$-independ…