New upper bound for hypercube slicing achieved using LLM-aided tool

Researchers have established a new upper bound for slicing hypercubes, improving upon a bound from 1971. The study proves that $S(n) \leq \lceil \frac{4n}{5} \rceil$ hyperplanes are sufficient to slice all edges of an $n$-dimensional hypercube, with a slight adjustment for cases where $n$ is an odd multiple of 5. This work also provides new lower bounds on the number of edges sliceable by fewer than $n$ hyperplanes. The improved upper bound was achieved through a construction aided by CPro1, a tool that leverages reasoning LLMs and automated hyperparameter tuning for discovering mathematical constructions. AI

IMPACT Demonstrates the utility of LLM-driven tools in advancing mathematical research and discovery.

RANK_REASON Academic paper published on arXiv detailing a new mathematical proof and construction. [lever_c_demoted from research: ic=1 ai=0.7]

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• CPro1
• Duncan Soiffer
• Paterson

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