Rational polynomials of simple type: a combinatorial proof

TL;DR

This paper provides a combinatorial proof to classify rational polynomials of simple type by determining their Newton trees, completing the existing classification framework.

Contribution

It offers a new combinatorial proof that fills a gap in the classification of rational polynomials of simple type.

Findings

Determined the Newton trees of rational polynomials of simple type.

Filled a gap in the classification proof by Neumann and Norbury.

Abstract

We determine the Newton trees of the rational polynomials of simple type, thus filling a gap in the proof of the classification of these polynomials given by Neumann and Norbury.