In [7, 10], the concept of pseudomatroid was developed as a proper generalization of the concept of matroid. The same concept was independently developed as ∆-matroid in [4, 5]. Throughout the paper, we use the more popular name ∆-matroid for this structure. In [6], the concept of ∆-matroid was further generalized to jump system. Further interesting results on jump system are reported in [1, 3,...

By combining the concepts of graviton and matroid, we outline a new gravitational theory which we call gravitoid theory. The idea of this theory emerged as an attempt to link the mathematical structure of matroid theory with M-theory. Our observations are essentially based on the formulation of matroid bundle due to MacPherson and Anderson-Davis. Also, by considering the oriented matroid theory...

Let H = (V, E) be a hypergraph and let k ≥ 1 and l ≥ 0 be fixed integers. LetM be the matroid with ground-set E s.t. a set F ⊆ E is independent if and only if each X ⊆ V with k|X| − l ≥ 0 spans at most k|X| − l hyperedges of F . We prove that if H is dense enough, thenM satisfies the double circuit property, thus the min-max formula of Dress and Lovász on the maximum matroid matching holds forM...

In this paper we consider the problem of finding the densest subset subject to co-matroid constraints. We are given a monotone supermodular set function f defined over a universe U , and the density of a subset S is defined to be f(S)/|S|. This generalizes the concept of graph density. Comatroid constraints are the following: given matroidM a set S is feasible, iff the complement of S is indepe...

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the u...