Related papers: A Theorem on Matroid Homomorphism

We continue the development of the infinitesimal deformation theory of pasting diagrams of k-linear categories begun in Yetter, D.N. "On Deformations of Pasting Diagrams", Theory and Applications of Categories 22 (2009) 24-53. In that…

This is a survey paper on spaces of automorphisms of manifolds and spaces of manifolds in a fixed homotopy type. It describes the main theorems of traditional surgery theory, but also the main theorems of pseudoisotopy theory, alias…

In 1980 Lov\'{a}sz introduced the concept of a double circuit in a matroid. The 2nd, 3rd and 4th authors recently generalised this notion to $k$-fold circuits (for any natural number $k$) and proved foundational results about these $k$-fold…

Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of direction constraints between the points is equivalent to 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…

We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular this allows us to characterize the homotopy colimits of diagrams of…

This paper introduces Dirichlet matroids, a generalization of graphic matroids arising from electrical networks. We present four main theorems. First, we exhibit a matroid quotient involving geometric duals of networks embedded in surfaces…

This note will become part of a new paper with more authors.

Based on the notion of vectors and linear subspaces for a matroid, we develop a theory of flats and hyperplane arrangements for T-matroids, where T is a tract. This leads to several cryptomorphic descriptions of T-matroids: in terms of its…

The fundamental theorem of geometry of rectangular matrices describes the general form of bijective maps on the space of all $m\times n$ matrices over a division ring $\mathbb{D}$ which preserve adjacency in both directions. This result…

A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…

We present exponential and super factorial lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graphs of a graphic, generalized Catalan and uniform matroids. All lower bounds were obtained by a common…

This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of…

We construct some matroids that have a circuit and a cocircuit with infinite intersection. This answers a question of Bruhn, Diestel, Kriesell, Pendavingh and Wollan. It further shows that the axiom system for matroids proposed by Dress…

Conditions for the existence of a fixed spectrum \{i.e., the set of fixed modes\} for a multi-channel linear system have been known for a long time. The aim of this paper is to reestablish one of these conditions using a new and transparent…

As part of the recent developments in infinite matroid theory, there have been a number of conjectures about how standard theorems of finite matroid theory might extend to the infinite setting. These include base packing, base covering, and…

We develop a theory of $\times$-homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that $\times$-homotopies from finite graphs can be decomposed…

We give a complete and detailed proof of Harer's stability theorem for the homology of mapping class groups of surfaces, with the best stability range presently known. This theorem and its proof have seen several improvements since Harer's…

Oriented matroids (often called order types) are combinatorial structures that generalize point configurations, vector configurations, hyperplane arrangements, polyhedra, linear programs, and directed graphs. Oriented matroids have played a…

In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.