A Natural Family of Flag Matroids

CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY MATROIDS AND FUZZIFYING MATROIDS

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...

Energy of Graphs, Matroids and Fibonacci Numbers

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.

Flag Matroids

Lagrangian Matroids: Representations of Type Bn

Coxeter matroids are combinatorial objects associated with finite Coxeter groups; they can be viewed as subsets M of the factor set W/P of a Coxeter group W by a parabolic subgroup P which satisfy a certain maximality property with respect to a family of shifted Bruhat orders on W/P . The classical matroids of matroid theory are exactly the Coxeter matroids for the symmetric group Symn (which i...

Matroids and Geometric Invariant Theory of Torus Actions on Flag Spaces

Title of dissertation: MATROIDS AND GEOMETRIC INVARIANT THEORY OF TORUS ACTIONS ON FLAG SPACES Benjamin Howard, Doctor of Philosophy, 2006 Dissertation directed by: Professor John Millson Department of Mathematics Let λ and μ be weights of G = SL(n,C) such that λ is dominant. Let Vλ be the irreducible representation of G with highest weight λ, and let Vλ[μ] denote the μ-th weight space within V...