Problem detail · source-aware
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How large can a Bruhat interval in $S_n$ that is a poset hypercube be? Using a permutation pattern suggested by AlphaEvolve, the authors exhibit hypercube intervals of dimension $O(n \log n)$ for $n$ a power of 2, matching the largest possible dimension up to a constant - in the problem circle around the combinatorial invariance conjecture for Kazhdan-Lusztig polynomials.
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AlphaEvolve, searching evolutionarily rather than exhaustively, "produced a pattern which performed well for the n tested, and which we show works well for general n" - the agent found the construction, the humans proved it works in general.
Provider: Google DeepMind · Prompt public: unknown · Independence: unknown
No verification note supplied.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Asymptotically optimal for powers of 2; the exact extremal answer for general n stays open.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.