The rank gradient from a combinatorial viewpoint

The rank gradient from a combinatorial viewpoint

This paper investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups in residually finite groups. We analyze three natural classes of groups: amenable groups, groups possessing an infinite soluble normal subgroup and virtually free groups. As a tool for the amenable case we generalize Lackenby’s trichotomy theorem on finitely presented groups.

3 1 Ja n 20 07 The rank gradient from a combinatorial viewpoint

This note investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups for three natural classes of groups: amenable groups, groups possessing an infinite soluble normal subgroup and virtually free groups.

Dedekind sums: a combinatorial-geometric viewpoint

Large scale combinatorial optimization: A methodological viewpoint

In this article, the author describes the results of a collaborative European project work with Abstract. The industrial and commercial worlds are increasingly competitive , requiring companiesto be more productiveand more responsiveto market changes (e.g. globalisation and privatisation). As a consequence, there is a strong need for solutions to large scale optimization problems, in domains su...

Computing the Permanental Polynomial of a Matrix from a Combinatorial Viewpoint

Recently, in the book [A Combinatorial Approach to Matrix Theory and Its Applications, CRC Press (2009)] the authors proposed a combinatorial approach to matrix theory by means of graph theory. In fact, if A is a square matrix over any field, then it is possible to associate to A a weighted digraph GA, called Coates digraph. Through GA (hence by graph theory) it is possible to express and prove...