Related papers: Thin sums matroids and duality

We introduce a connectivity function for infinite matroids with properties similar to the connectivity function of a finite matroid, such as submodularity and invariance under duality. As an application we use it to extend Tutte's linking…

A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…

We give new characterizations for the class of uniformly dense matroids and study applications of these characterizations to graphic and real representable matroids. We show that a matroid is uniformly dense if and only if its base polytope…

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…

We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network. We exhibit a…

We introduce the notion of sum-matroids and show its association with sum-rank metric codes. As a consequence, some results for sum-rank metric codes by Mart\'inez-Pe\~nas are generalized for sum-matroids. The sum-matroids generalize the…

Seymour's Decomposition Theorem for regular matroids states that any matroid representable over both GF(2) and GF(3) can be obtained from matroids that are graphic, cographic, or isomorphic to R10 by 1-, 2-, and 3-sums. It is hoped that…

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…

Recently, Gross, Mansour and Tucker introduced the partial duality polynomial of a ribbon graph and posed a conjecture that there is no orientable ribbon graph whose partial duality polynomial has only one non-constant term. We found an…

We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, oriented matroids, and regular matroids. To do this, we first introduce algebraic objects called tracts which…

For classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for $q$-matroids, the $q$-analogue of matroids. This is a lot less straightforward…

q-Matroids form the q-analogue of classical matroids. In this paper we introduce various types of maps between q-matroids. These maps are not necessarily linear, but they map subspaces to subspaces and respect the q-matroid structure in…

We prove that the topological cycles of an arbitrary infinite graph induce a matroid. This matroid in general is neither finitary nor cofinitary.

We introduce ideas that complement the many known connections between polymatroids and graph coloring. Given a hypergraph that satisfies certain conditions, we construct polymatroids, given as rank functions, that can be written as sums of…

Frame matroids and lifted-graphic matroids are two interesting generalizations of graphic matroids. Here we introduce a new generalization, {\em quasi-graphic matroids}, that unifies these two existing classes. Unlike frame matroids and…

We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis activities, and we prove some basic structural…

Blasiak verified a conjecture of White for graphic matroids by showing that the toric ideal of a graphic matroid is generated by quadrics. In this paper, we extend this result to frame matroids satisfying a linearity condition. Such classes…

In this paper we associate with an infinite family of real extended functions defined on a locally convex space, a sum, called robust sum, which is always well-defined. We also associate with that family of functions a dual pair of problems…

We generalize the well-studied notion of a modular pair of a finite matroid to arbitrary families of sets in infinite matroids, and use it to develop the theory of infinite matroids in several as-yet-unexplored areas. Our results include a…

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…