6 citations · 21 across the 16 of their papers we have counts for
12 papers · 1 filter
Duals of algebraic matroids need not be algebraic
Matt Larson, Tuong Le
We give an example showing that the dual of an algebraic matroid need not be algebraic. Our example is a matroid of rank 6 on 10 elements which is algebraic in characteristic 2. It…
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…
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…
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…
Kazhdan-Lusztig polynomials of braid matroids
Luis Ferroni, Matt Larson
We provide a combinatorial interpretation of the Kazhdan--Lusztig polynomial of the matroid arising from the braid arrangement of type , which gives an interpreta…
Resolutions of local face modules, functoriality, and vanishing of local -vectors
Matt Larson, Sam Payne, Alan Stapledon
We study the local face modules of triangulations of simplices, i.e., the modules over face rings whose Hilbert functions are local -vectors. In particular, we give resolutions…
The Bergman fan of a polymatroid
Colin Crowley, June Huh, Matt Larson +2
We introduce the Bergman fan of a polymatroid and prove that the Chow ring of the Bergman fan is isomorphic to the Chow ring of the polymatroid. Using the Bergman fan, we establish…
Inverse problems for minimal complements and maximal supplements
Noga Alon, Noah Kravitz, Matt Larson
Given a subset of an abelian group , a subset is called an additive complement for if ; if, moreover, no proper subset of has this property, then we say t…
Power maps in finite groups
Matt Larson
In recent work, Pomerance and Shparlinski have obtained results on the number of cycles in the functional graph of the map in . We prove similar res…
Union of Random Trees and Applications
Austen James, Matthew Larson, Daniel Montealegre +1
In 1986, Janson showed that the number of edges in the union of random spanning trees in the complete graph is a shifted Poisson distribution. Using results from the theo…