For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number. If one considers two simple closed curves L and S on a closed orientable surface F , one can define their intersection number to be the least number of intersection points obtainable b...

We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety G defined over a finite field with a closed subvariety X ⊂ G.

In this paper we begin the classification completed in [12] of all partial linear spaces n , graphs F, and groups G which satisfy one of the following: I. II = (0>, ££) is a connected partial linear space of order 2 in which every pair of intersecting lines lies in a subspace isomorphic to the dual of an affine plane of order 2; II. F is a connected graph such that, for each vertex x of F, the ...

A disk graph is the intersection graph of disks in the plane, a unit disk graph is the intersection graph of same radius disks in the plane, and a segment graph is an intersection graph of line segments in the plane. Every disk graph can be realized by disks with centers on the integer grid and with integer radii; and similarly every unit disk graph can be realized by disks with centers on the ...

Abstract We give sufficient conditions to ensure that the intersection of product two subgroups A and B a group G with an abelian normal subgroup K is .

We extend the notion of a minor from matroids to simplicial complexes. We show that the class of matroids, as well as the class of independence complexes, is characterized by a single forbidden minor. Inspired by a recent result of Aharoni and Berger, we investigate possible ways to extend the matroid intersection theorem to simplicial complexes.

In this paper, we show that for any independence system, the problem of finding a persistency partition of the ground set and that of finding a maximum weight independent set are polynomially equivalent.

We present a systematic study of the expected complexity of the intersection of geometric objects. We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target o...

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number. AMS Classification numbers Primary: 20F32 Secondary: 20E06, 20E07, 20E08, 57M07

We consider a generalization of edge intersection graphs of paths in a tree. Let P be a collection of nontrivial simple paths in a tree T . We define the k-edge (k 1) intersection graph k(P), whose vertices correspond to the members of P, and two vertices are joined by an edge if the corresponding members ofP share k edges in T . An undirected graphG is called a k-edge intersection graph of pat...