Analog of the Cayley–Sylvester formula and the Poincaré series for an algebra of invariants of ternary form

Abstract

An explicit formula is obtained for the number $ν_d(n)$ of linearly independent homogeneous invariants of degree $n$ of a ternary form of order $d$. A formula for the Poincaré series of the algebra of invariants of the ternary form is also deduced.