Related papers: Nearly Finitary Matroids
We introduce a new model for the realization space of a matroid, which is obtained from a variety defined by a saturated determinantal ideal, called the slack ideal, coming from the vertex-hyperplane incidence matrix of the matroid. This is…
In this paper, we design fixed-parameter tractable (FPT) algorithms for (non-monotone) submodular maximization subject to a matroid constraint, where the matroid rank $r$ is treated as a fixed parameter that is independent of the total…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
In this paper we consider quasi-concave set functions defined on antimatroids. There are many equivalent axiomatizations of antimatroids, that may be separated into two categories: antimatroids defined as set systems and antimatroids…
The property of balance (in the sense of Feder and Mihail) is investigated in the context of paving matroids. The following examples are exhibited: (a) a class of ``sparse'' paving matroids that are balanced, but at the same time rich…
In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics and the rigidity theory of bar-and-joint frameworks. In each…
An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neither matroid can be obtained, up to isomorphism, from the other…
The multilinear framework has achieved the breakthrough $1-1/e$ approximation for maximizing a monotone submodular function subject to a matroid constraint. This framework has a continuous optimization part and a rounding part. We extend…
In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization in [BS18a] to quantify the information theoretic…
One of the simplest axiomatizations of a matroid is in terms of independent sets. Curiously, no such independent set axiomatization is known for Gelfand and Serganova's WP-matroids (which are ``Coxeter group analogues'' of matroids). Here…
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…
Symmetric powers of matroids were first introduced by Lovasz and Mason in the 1970s, where it was shown that not all matroids admit higher symmetric powers. Since these initial findings, the study of matroid symmetric powers has remained…
We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…
The ground set for all matroids in this paper is the set of all edges of a complete graph. The notion of a {\it maximum matroid for a graph} $G$ is introduced, and the existence and uniqueness of the maximum matroid for any graph $G$ is…
A new isomorphism invariant of matroids is introduced, in the form of a quasisymmetric function. This invariant (1) defines a Hopf morphism from the Hopf algebra of matroids to the quasisymmetric functions, which is surjective if one uses…
In this article, we investigate the multi-parametric matroid problem. The weights of the elements of the matroid's ground set depend linearly on an arbitrary but fixed number of parameters, each of which is taken from a real interval. The…
We consider three forms of composition of matroids, each of which extends the category of bimatroids to a rigid monoidal category. Many well-known constructions are functorial or defined by morphisms in these categories. Motivating examples…
In the matroid secretary problem we are given a stream of elements and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from…
This paper compares skew-linear and multilinear matroid representations. These are matroids that are representable over division rings and (roughly speaking) invertible matrices, respectively. The main tool is the von Staudt construction,…
We consider three matroids defined by Kalai in 1985: the symmetric completion matroid $\mathcal{S}_d$ on the edge set of a looped complete graph; the hyperconnectivity matroid $\mathcal{H}_d$ on the edge set of a complete graph; and the…