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Poincaré series of the multigraded algebras of SL 2-invariants

We deduce formulas for finding the Poincaré multiseries \( \mathcal{P}\left( {{\mathcal{C}_d},{z_1},{z_2}, \ldots, {z_n},t} \right) \) and \( \mathcal{P}\left( {{\mathcal{I}_d},{z_1},{z_2}, \ldots, {z_n}} \right) \), where \( {\mathcal{C}_d} \) and \( {\mathcal{I}_d} \), d = (d 1, d 2, . . . , d n ), are multigraded algebras of joint covariants and joint invariants for n binary forms of degrees d 1, d 2, . . . , d n .

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Author information

Correspondence to L. P. Bedratyuk.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 6, pp. 755–763, June, 2011.

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Bedratyuk, L.P. Poincaré series of the multigraded algebras of SL 2-invariants. Ukr Math J 63, 880–890 (2011). https://doi.org/10.1007/s11253-011-0550-8

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Keywords

  • Invariant Theory
  • Formal Power Series
  • Binary Form
  • Symmetric Algebra
  • Coordinate Algebra