A129550 Number of real polynomial invariants for the action of 4 copies of U(2) on the fourth tensor power of C^2.

1, 1, 8, 20, 98, 293, 1128, 3409, 10846, 30480, 84652, 217677, 544312, 1289225, 2961626, 6528284, 13980717, 28963980, 58464510, 114806429, 220298632, 412950779, 758418342, 1365044296, 2412766496, 4189995629, 7159916414

Offset: 0

Author

Mike Zabrocki, Apr 20 2007

Keywords

• nonn

References

• M. W. Hero and J. F. Willenbring, Stable Hilbert series as related to the measurement of quantum entanglement, Discrete Math., 309 (2010), 6508-6514.
• Nolan R. Wallach, The Hilbert series for measures of entanglement in 4 qubits, Acta Appl. Math. 86(2005),203-220.

Crossrefs

Cf. A129548, A129549.

Formula

G.f.: (R(q) + q^76*R(1/q))/((1 - q^2)*(1 - q^4)^7*(1 - q^6)^6*(1 - q^8)^4*(1 - q^10)) where R(q) = 1 + 6*q^6 + 46*q^8 + 110*q^10 + 344*q^12 + 844*q^14 + 2154*q^16 + 4606*q^18 + 9397*q^20 + 16848*q^22 + 28747*q^24 + 44580*q^26 + 65366*q^28 + 88036*q^30 + 111909*q^32 + 131368*q^34 + 145676*q^36 + 149860/2*q^38.