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Is the sequence $W_0, W_1, \dots, W_n$ counting the flats of each rank of a matroid always unimodal? Rota conjectured yes in 1970.
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A counterexample to the convexity of the sequence $W_i^{-1}$ was found with ChatGPT-5.6 Pro following a suggestion of the authors. This matroid was constructed using Whittle's $q$-lift mechanism, which the authors then adapted into a counterexample for unimodality.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Public arXiv preprint with explicit counterexamples, checked by the human authors. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.