A036983 Number of invariants in Hilbert basis for binary forms of degree n.

1, 1, 2, 4, 5, 30, 9, 92, 106

Offset

2,3

Comments

Extending this is related to a "gorgeous open question of great antiquity" [Towber].

Comment "The linear form has no invariants. The binary quadratic and cubic only have one invariant." by Abdelmalek Abdesselam, Nov 26, 2017 to MathOverflow question 286872. - Michael Somos, Nov 02 2023

References

Roe Goodman and Nolan R. Wallach, Representations and invariants of the classical groups, Cambridge Univ. Press, Cambridge, 1998

P. J. Olver, Classical Invariant Theory, Cambridge Univ. Press, p. 40.

Links

Table of n, a(n) for n=2..10.

A. E. Brouwer and M. Popoviciu, The invariants of the binary nonic, J. Symb. Comput. 45 (2010) 709-720.

A. E. Brouwer and M. Popoviciu, The invariants of the binary decimic, J. Symb. Comput. 45 (2010) 837-843.

MathOverflow, What is currently feasible in invariant theory for binary forms? question 286872, Nov 24, 2017.

J. Towber, Review of "Representations and Invariants of the Classical Groups" by Roe Goodman and Nolan R. Wallach, Bull. Amer. Math. Soc., 36 (1999), 533-538.

Wikipedia, Invariant of a binary form.

Crossrefs

Cf. A036984.

Sequence in context: A277371 A199929 A126666 * A370438 A303006 A154775

Adjacent sequences: A036980 A036981 A036982 * A036984 A036985 A036986

Keyword

nonn,nice,hard,more

Author

N. J. A. Sloane

Extensions

a(9)-a(10) from Andries E. Brouwer, Feb 17 2015

First term 0 removed by Michael Somos, Nov 02 2023

Status

approved