JCT
2010
12 years 11 months ago
2010
There exist several theorems which state that when a matroid is representable over distinct fields 1,..., k, it is also representable over other fields. We prove a theorem, the Li...
SIAMDM
2011
12 years 11 months ago
2011
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, o...
EJC
2011
12 years 11 months ago
2011
Abstract. We introduce a new axiomatization of oriented matroids that requires the elimination property only among modular pairs of circuits. This new point of view leads also to a...
JCT
2010
13 years 3 months ago
2010
A lattice path matroid is a transversal matroid for which some antichain of intervals in some linear order on the ground set is a presentation. We characterize the minor-closed cla...
EJC
2008
13 years 3 months ago
2008
A matroid M is sequential or has path width 3 if M is 3-connected and its ground set has a sequential ordering, that is, an ordering (e1, e2, . . . , en) such that ({e1, e2, . . . ...
DM
2002
13 years 4 months ago
2002
For each prime p, we construct an infinite antichain of matroids in which each matroid has characteristic set {p}. For p = 2, each of the matroids in our antichain is an excluded m...
DCG
2000
13 years 4 months ago
2000
Several polynomials are of use in various enumeration problems concerning objects in oriented matroids. Chief among these is the Radon catalog. We continue to study these, as well ...
COMBINATORICS
2002
13 years 4 months ago
2002
Knowing the excluded minors for a minor-closed matroid property provides a useful alternative characterization of that property. It has been shown in [R. Hall, J. Oxley, C. Semple...
JCT
2007
13 years 4 months ago
2007
Abstract. We develop linear representation theory for bicircular matroids, a chief example being a matroid associated with forests of a graph, and bicircular lift matroids, a chief...
TIT
2008
13 years 4 months ago
2008
Error-correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes. In this paper, the connections between codes, matroids, and a special cla...