We prove that, given integers l, q ≥ 2 and n there exists an integer α such that, if M is a simple matroid with no l + 2point line minor and at least αq elements, then M contains a PG(n− 1, q′)-minor, for some prime-power q′ > q.

A coxeter matroid is a generalization of matroid, ordinary matroid being the case corresponding to the family of Coxeter groups An , which are isomorphic to the symmetric groups. A basic result in the subject is a geometric characterization of Coxeter matroid in terms of the matroid polytope, a result first stated by Gelfand and Serganova. This paper concerns properties of the matroid polytope....

There are many symmetries in intuitionistic fuzzifying topology. In the present paper, notion of topology as an extension and a preliminary research on bi-intuitionistic fuzzy is introduced. A theory with semantic method logic established.

Matroid theory is in the center of Combinatorics, Finite Geometry, Lattice theory and Combinatorial Optimization. During the last decades, extensive search was done in order to find a good degree of generality which still preserves the validity of deep results known for matroids. One of such generalizations is the concept of bouquet of matroids introduced in 1983 by Deza, Frank1 and Laurent and...

The Constraint Hierarchy (CH) framework is used to tackle multiple criteria selection (MCS), consisting of a set of candidates and a set of, possibly competing, criteria for selecting the \best" candidate(s). In this paper, we identify aspects of the CH framework for further enhancement so as to model and solve MCS problems more accurately. We propose the Fuzzy Constraint Hierarchies framework,...

The aim of this paper is to study the categorical relations betweenmatroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids.It is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. The category of matroids can be embedded in that offuzzifying matroids as a simul...

A new matroid is introduced: this matroid is de0ned starting from any matroid and one of its bases, hence we call it base-matroid. Besides some properties of the base-matroid, a non-trivial algorithm for the solution of the related matroid optimization problem is presented. The new matroid has application in the 0eld of inverse combinatorial optimization problems. We discuss in detail the LP fo...

1. Introduction. In a recent series of papers [l-4] on graphs and matroids I used definitions equivalent to the following. A binary chain-group N on a. finite set M is a class of subsets of M forming a group under mod 2 addition. These subsets are the chains of N. A chain of N is elementary if it is non-null and has no other non-null chain of AT as a subset. A binary matroid is the class of ele...

One may regard vectors in a finite dimensional vector space as being linear forms in a polynomial ring in an obvious way. A collection of linear forms satisfying various linear dependence relations can become independent when each of the forms is raised to the k-th power. In this paper we prove that a certain class of matroids satisfies a " higher order " independence property of this kind. The...