6 citations · 21 across the 16 of their papers we have counts for
20 papers
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…
Cohomological aspects of power ideals
Colin Crowley, Matt Larson
We show that the space of sections of any line bundle on the augmented wonderful variety of a hyperplane arrangement has the structure of a coalgebra. These coalgebras correspond t…
Kapranov degrees
Joshua Brakensiek, Christopher Eur, Matt Larson +1
The moduli space of stable rational curves with marked points has two distinguished families of maps: the forgetful maps, given by forgetting some of the markings, and the Kapranov…
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…
Intersection theory of polymatroids
Christopher Eur, Matt Larson
Polymatroids are combinatorial abstractions of subspace arrangements in the same way that matroids are combinatorial abstractions of hyperplane arrangements. By introducing augment…
-rings of wonderful varieties and matroids
Matt Larson, Shiyue Li, Sam Payne +1
We study the -ring of the wonderful variety of a hyperplane arrangement and give a combinatorial presentation that depends only on the underlying matroid. We use this combinator…
Signed permutohedra, delta-matroids, and beyond
Christopher Eur, Alex Fink, Matt Larson +1
We establish a connection between the algebraic geometry of the type B permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the vo…
The local motivic monodromy conjecture for simplicial nondegenerate singularities
Matt Larson, Sam Payne, Alan Stapledon
We prove the local motivic monodromy conjecture for singularities that are nondegenerate with respect to a simplicial Newton polyhedron. It follows that all poles of the local topo…
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…
Stellahedral geometry of matroids
Christopher Eur, June Huh, Matt Larson
We use the geometry of the stellahedral toric variety to study matroids. We identify the valuative group of matroids with the cohomology ring of the stellahedral toric variety, and…
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…
The Arakelov-Zhang pairing and Julia sets
Andrew Bridy, Matt Larson
The Arakelov-Zhang pairing is a measure of the "dynamical distance" between two rational maps and defined over a number field . It is defined in term…
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…