Unimodality of Kazhdan-Lusztig Polynomials of Matroids
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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.
Context
Gedeon-Proudfoot-Young conjectures in the June Huh school's active program.
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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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