EJC
2000
13 years 4 months ago
2000
Consider the moment curve in the real Euclidean space Rd defined parametrically by the map : R Rd , t (t) = (t, t2 , . . . , td ). The cyclic d-polytope Cd(t1, . . . , tn) is t...
CPC
2000
13 years 4 months ago
2000
We examine the specialization to simple matroids of certain problems in extremal matroid theory that are concerned with bounded cocircuit size. Assume that each cocircuit of a simp...
JUCS
2007
13 years 4 months ago
2007
: Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures...
JCT
2007
13 years 4 months ago
2007
Abstract. We prove that a binary matroid with huge branchwidth contains the cycle matroid of a large grid as a minor. This implies that an infinite antichain of binary matroids ca...
JCT
2006
13 years 4 months ago
2006
Abstract. We introduce "matroid parse trees" which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounde...
JCT
2006
13 years 4 months ago
2006
The cocircuit graph of an oriented matroid is the 1-skeleton of the cellular decomposition induced by the Topological Representation Theorem due to Folkman and Lawrence (1978) [J....
JCT
2006
13 years 4 months ago
2006
We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural su...
COMBINATORICS
2007
13 years 4 months ago
2007
Let F4 be the root system associated with the 24-cell, and let M(F4) be the simple linear dependence matroid corresponding to this root system. We determine the automorphism group...
DM
2006
13 years 5 months ago
2006
Given a 3-connected biased graph with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of is uniquely represented by .
DM
2006
13 years 5 months ago
2006
Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view Dowling lattices and ne...