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

ar X iv : m at h . C O / 0 41 04 25 v 1 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 : m at h / 06 09 42 6 v 3 [ m at h . C O ] 1 5 O ct 2 00 6 SUM - PRODUCT ESTIMATES IN FINITE FIELDS VIA KLOOSTERMAN

We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.

ar X iv : m at h / 04 10 21 7 v 1 [ m at h . C O ] 8 O ct 2 00 4 Joints in graphs

In 1969 Erd˝ os proved that if r ≥ 2 and n > n0 (r) , every graph G of order n and e (G) > tr (n) has an edge that is contained in at least n r−1 / (10r) 6r (r + 1)-cliques. In this note we improve this bound to n r−1 /r r+5. We also prove a corresponding stability result.

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