Topological enumeration of complex polynomial vector fields

Abstract

The enumeration of combinatorial classes of the complex polynomial vector fields in C presented in [Dia13] is extended here to a closed form enumeration of combinatorial classes for degree d polynomial vector fields up to rotations of 2(d-1)st roots of unity. The main tool in the proof of this result is based on a general method of enumeration developed by V.A.Liskovets [Lis98].