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

• Date: 2010
• Main Authors: Bedratyuk, L. P., Бедратюк, Л. П.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2980
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.