Problems / combinatorics

combinatorics / Algebraic combinatorics

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.