Unimodality of Kazhdan-Lusztig Polynomials of Matroids

Precise statement

Are the Kazhdan-Lusztig polynomials of matroids always unimodal - in particular log-concave, or even real-rooted, as conjectured? No: representable matroids obtained by deleting points from finite projective geometries have non-unimodal Kazhdan-Lusztig polynomials over every finite field, so the log-concavity and real-rootedness conjectures are both false.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

Rethlas agent (GPT-5.6 Sol)

The result came from running the Rethlas research agent with base model GPT-5.6 Sol at maximum reasoning effort - the same agent behind the Analytic Bertini entry; the paper documents the run and the authors verified the constructions.

Provider: unknown · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

arXiv preprint (v2) with explicit constructions from projective geometries; not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-27

   arXiv:2607.24186 - Kazhdan-Lusztig polynomials of matroids need not be unimodal

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.