Topological enumeration of complex polynomial vector fields

TL;DR

This paper extends the enumeration of combinatorial classes of complex polynomial vector fields in C to a closed form, considering rotations, using a method developed by Liskovets.

Contribution

It provides a closed form enumeration of combinatorial classes for degree d polynomial vector fields up to rotations, expanding previous work.

Findings

Derived a closed form enumeration formula

Extended enumeration to include rotational symmetries

Utilized Liskovets' enumeration method

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].