ar X iv : m at h . C O / 0 41 04 25 v 1 1 9 O ct 2 00 4 MULTI - PATH MATROIDS

ar X iv : m at h / 04 10 42 5 v 1 [ m at h . C O ] 1 9 O ct 2 00 4 MULTI - PATH MATROIDS

We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis activities, and we prove some basic structural properties. Key elements of this work are two complementary perspectives we develop for these matroids: on the one hand, multi-path matroids are transversal ...

ar X iv : m at h / 04 03 33 7 v 1 [ m at h . C O ] 2 1 M ar 2 00 4 LATTICE PATH MATROIDS : STRUCTURAL PROPERTIES

This paper studies structural aspects of lattice path matroids, a class of transversal matroids that is closed under taking minors and duals. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One of the main results is a characterization of lattice path matroids in terms of fundamental flats, which are special connected flats from which one can recove...

ar X iv : h ep - t h / 04 10 18 8 v 1 18 O ct 2 00 4 Spacetime quantization induced by axial currents

ar X iv : m at h / 04 10 34 7 v 1 [ m at h . C O ] 1 5 O ct 2 00 4 COMPLETING A k − 1 ASSIGNMENT

We consider the distribution of the value of the optimal k-assignment in an m× n-matrix, where the entries are independent exponential random variables with arbitrary rates. We give closed formulas for both the Laplace transform of this random variable and for its expected value under the condition that there is a zero-cost k − 1-assignment.

ar X iv : m at h / 04 10 61 1 v 1 [ m at h . A G ] 2 8 O ct 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES