The degrees of a system of parameters of the ring of invariants of a binary form

TL;DR

This paper investigates the degrees of elements in a homogeneous system of parameters for the invariant ring of binary forms, providing divisibility conditions and a complete classification for degrees up to 8.

Contribution

It introduces a divisibility condition for the degrees and classifies all cases for binary forms of degree at most 8.

Findings

Established divisibility conditions for degrees of parameters.

Provided a complete classification for degrees ≤ 8.

Enhanced understanding of invariant rings of binary forms.

Abstract

We consider the degrees of the elements of a homogeneous system of parameters for the ring of invariants of a binary form, give a divisibility condition, and a complete classification for forms of degree at most 8.