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Unimodality of Kazhdan-Lusztig Polynomials of Matroids

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.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jul 27, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Unimodality of Kazhdan-Lusztig Polynomials of Matroids · KL matroid unimodality

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Ronnie Cheng
human · human collaborator

Shurui Liu
human · human collaborator

Rethlas agent (GPT-5.6 Sol)
model · ai model contributor

Lineage and corrections

This event attributed to Shurui Liu

This event attributed to Ronnie Cheng

This event attributed to Rethlas agent (GPT-5.6 Sol)

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