Consider the moment curve in the real Euclidean space Rd defined parametrically by the map : R Rd , t (t) = (t, t2 , . . . , td ). The cyclic d-polytope Cd(t1, . . . , tn) is t...
We examine the specialization to simple matroids of certain problems in extremal matroid theory that are concerned with bounded cocircuit size. Assume that each cocircuit of a simp...
: Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures...
Abstract. We prove that a binary matroid with huge branchwidth contains the cycle matroid of a large grid as a minor. This implies that an infinite antichain of binary matroids ca...
Abstract. We introduce "matroid parse trees" which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounde...
The cocircuit graph of an oriented matroid is the 1-skeleton of the cellular decomposition induced by the Topological Representation Theorem due to Folkman and Lawrence (1978) [J....
We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural su...
Let F4 be the root system associated with the 24-cell, and let M(F4) be the simple linear dependence matroid corresponding to this root system. We determine the automorphism group...
Stephanie Fried, Aydin Gerek, Gary Gordon, Andrija...
Given a 3-connected biased graph with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of is uniquely represented by .
Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view Dowling lattices and ne...