5 papers · 1 filter
Matroid flat counts can have many peaks
Alexander Divoux, Matt Larson, Chayim Lowen +1
We disprove Rota's conjecture that the counts of flats in a matroid according to rank form a unimodal sequence. Furthermore, we show that this sequence can have arbitrarily many pe…
Counterexamples to two conjectures about matroids
Matt Larson
We give counterexamples to two well-known conjectures about matroids: White's conjecture on the generation of the toric ideal by symmetric exchange binomials, and a conjecture of M…
Kazhdan-Lusztig polynomials of Dowling geometries
Luis Ferroni, Matt Larson
We give a concrete combinatorial interpretation of the coefficients of the Kazhdan-Lusztig polynomials of Dowling geometries, a family of matroids which generalizes braid matroids…
Rank functions and invariants of delta-matroids
Matt Larson
In this note, we give a rank function axiomatization for delta-matroids and study the corresponding rank generating function. We relate an evaluation of the rank generating functio…
K-classes of delta-matroids and equivariant localization
Christopher Eur, Matt Larson, Hunter Spink
Delta-matroids are "type B" generalizations of matroids in the same way that maximal orthogonal Grassmannians are generalizations of Grassmannians. A delta-matroid analogue of the…