ESA
2011
Springer
12 years 10 months ago
2011
Springer
We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the “rando...
JCT
2010
13 years 5 months ago
2010
Let M be a matroid representable over a (partial) field and B a matrix representable over a sub-partial field . We say that B confines M to if, whenever a -representation matrix ...
JCT
2010
13 years 9 months ago
2010
Abstract. For each finite field F of prime order there is a constant c such that every 4-connected matroid has at most c inequivalent representations over F. We had hoped that th...
JCT
2010
13 years 9 months ago
2010
We prove that every 3-connected GF(q)-representable matroid that contains the projective plane, PG(2, q), as a minor is uniquely representable.
JCT
2008
13 years 9 months ago
2008
Let {a, b, c} be a triangle in a 3-connected matroid M. In this paper, we describe the structure of M relative to {a, b, c} when, for all t in {a, b, c}, either M\t is not 3-connec...
DM
1998
13 years 10 months ago
1998
We give a counterexample to a conjecture by Wild about binary matroids. We connect two equivalent lines of research in matroid theory: a simple type of basis-exchange property and ...
COMBINATORICS
1998
13 years 10 months ago
1998
A multimatroid is a combinatorial structure that encompasses matroids, delta-matroids and isotropic systems. This structure has been introduced to unify a theorem of Edmonds on th...
ENTCS
2002
13 years 10 months ago
2002
The aim of this work is to show that (oriented) matroid methods can be applied to many discrete geometries, namely those based on modules over integral (ordered) domains. The tric...
EJC
2002
13 years 10 months ago
2002
A cycle in a matroid is a disjoint union of circuits. This paper proves that every regular matroid M without coloops has a set S of cycles whose union is E(M) such that every elem...
EJC
2002
13 years 10 months ago
2002
The Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal (M) generated by the boundaries of the circuits of the matroid. There i...