The Poincare series for the algebra of invariants of $n$-ary form

TL;DR

This paper derives a formula for the Poincare series of the algebra of invariants associated with n-ary forms, providing a mathematical tool for understanding their structure.

Contribution

It presents a new explicit formula for the Poincare series of invariants of n-ary forms, advancing algebraic invariant theory.

Findings

Derived the formula for the Poincare series

Enhanced understanding of invariants of n-ary forms

Provided a mathematical foundation for further research

Abstract

The formula for the Poincare series of the algebra of invariant of $n$-ary form is found.