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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 11, pp. 1561–1570, November, 2010.
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Bedratyuk, L.P. Analog of the Cayley–Sylvester formula and the Poincaré series for an algebra of invariants of ternary form. Ukr Math J 62, 1810–1821 (2011). https://doi.org/10.1007/s11253-011-0470-7
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DOI: https://doi.org/10.1007/s11253-011-0470-7