Analogue of Sylvester-Cayley formula for invariants of ternary form

TL;DR

This paper calculates the number of linearly independent homogeneous invariants of a given degree for ternary forms of a specific degree, extending classical invariant theory results.

Contribution

It provides a formula for counting invariants of ternary forms, offering a new analogue of the Sylvester-Cayley formula.

Findings

Derived a formula for $ u_d(n)$

Extended classical invariant theory results

Provided explicit calculations for specific degrees

Abstract

The number $\nu_d(n)$ of linearly independed homogeneous invariants of degree $n$ for the ternary form of degree $d$ is calculated.