Unimodality of Kazhdan-Lusztig Polynomials of Matroids
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.
Record
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construction · #1
Rethlas agent (GPT-5.6 Sol), with Ronnie Cheng and Shurui LiuThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
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.
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