On first experiences with the implementation of a Newton based linear programming approach

Available from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Matroiderweiterungen zur Existenz endlicher LP-Algorithmen, von Hahn-Banach-Sätzen und Polarität in orientierten Matroiden

Hauptanliegen dieser Arbeit ist, verschiedene Schnittbedingungen in der (orientieren) Matroid-Theorie zu etablieren, durch unendlich viele verschiedene Matroide zu unterscheiden und diverse Folgerungen der einzelnen Schnittbedingungen fuer die Polyedertheorie orientierter Matroide abzuleiten

Separation Theorems for Oriented Matroids

In this paper we show that Minty's lemma can be used to prove the Hahn-Banach theorem as well as other theorems in this class such as Radon's and Helly's theorem for oriented matroids having an intersection property which guarantees that every pair of flats intersects in some point extension {cal O}cup p of the oriented matroid {cal O}

Euclidean Intersection Properties

There are matroids which have Euclidean and non-Euclidean orientations and there are also matroids whose inherent structure does not allow any Euclidean orientation. In this paper we discuss some lattice theoretic properties of matroids which when used in an oriented version guarantee Euclideanness. These properties depend all on the existence of intersections of certain flats (which is equivalent to Euclideanness interpreted in the Las Vergnas notation of oriented matroids). We introduce three classes of matroids having various intersection properties and show that two of them cannot be characterized by excluding finitely many minors

On a problem about covering lines by squares

Let S be the square [0,n]^2 of side length nin {f N} and let {cal S}={ S_1,ldots,S_t} be a set of unit squares lying inside S, whose sides are parallel to those of S. The set cal S is called a line cover, if every line intersecting S also intersects some S_iin {cal S}. Let au (n) denote the minimum cardinality of a line cover, and let au '(n) be defined in the same way, except that we restrict our attention to lines which are parallel to either one of the axes or one of the diagonals of S. It has been conjectured by L.F. Tôth that au (n)=2n+0(1) and I. Barányi and Z. Füredi that au (n)={3over 2}n+0(1). We will prove instead, au '(n)={4over 3}+0(1), and as to Tôth's conjecture, we will exhibit a ''non integerŜŜ solution to a related LP-relaxation, which has size equal to {3over 2}+0(1)

On a problem about covering lines by squares

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel C 145399 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Matroids without adjoint

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel C 146346 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Matroids without Adjoint

The purpose of this note is to give an example of a rank-4 matroid which not only shows that Levi's intersection property is not a sufficient condition for the existence of an adjoint but also seems to have an interesting structure of the lattice of flats