相关论文: Well-Scaling Procedure for Deciding Gammoid Class-…
A matroid $M$ is an ordered pair $(E,I)$, where $E$ is a finite set called the ground set and a collection $I\subset 2^{E}$ called the independent sets which satisfy the conditions: (i) $\emptyset \in I$, (ii) $I'\subset I \in I$ implies…
In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid.…
A binary frame template is a device for creating binary matroids from graphic or cographic matroids. Such matroids are said to conform or coconform to the template. We introduce a preorder on these templates and determine the nontrivial…
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal…
For a given selection of rows and columns from a Fourier matrix, we give a number of tests for whether the resulting submatrix is Hadamard based on the primitive sets of those rows and columns. In particular, we demonstrate that whether a…
We study the matroid secretary problems with submodular valuation functions. In these problems, the elements arrive in random order. When one element arrives, we have to make an immediate and irrevocable decision on whether to accept it or…
We study the algebraic matroid induced by the ideal of (r+1)-minors of a matrix of variables over a field. This is inherently connected to the bounded-rank matrix completion problem, in which the aim is to complete a partially observed rank…
In this paper we give a necessary and sufficient criterion for representability of a matroid over an algebraic closed field. This leads to an algorithm, based on an extension of Groebner Bases, in order to decide if a given matroid is…
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…
A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept. One natural way to obtain matroids is by considering…
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…
We introduce the parametric matroid one-interdiction problem. Given a matroid, each element of its ground set is associated with a weight that depends linearly on a real parameter from a given parameter interval. The goal is to find, for…
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…
This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…
We study paving matroids, their realization spaces, and their closures, along with matroid varieties and circuit varieties. Within this context, we introduce three distinct methods for generating polynomials within the associated ideals of…
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…
In a matroid secretary problem, one is presented with a sequence of objects of various weights in a random order, and must choose irrevocably to accept or reject each item. There is a further constraint that the set of items selected must…
In this work we present an algorithm to construct sparse-paving matroids over finite set $S$. From this algorithm we derive some useful bounds on the cardinality of the set of circuits of any Sparse-Paving matroids which allow us to prove…
We study rank-three matroids, known as point-line configurations, and their associated matroid varieties, defined as the Zariski closures of their realization spaces. Our focus is on determining finite generating sets of defining equations…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…