A318205 a(n) is the number of integer partitions of n for which the rank is equal to the index of the seaweed algebra formed by the integer partition paired with its weight.

1, 1, 2, 1, 1, 2, 2, 5, 2, 7, 7, 6, 10, 12, 12, 16, 14, 22, 27, 28, 44, 52, 61, 76, 93, 112, 135, 162, 209, 243, 300, 350, 425, 484, 600, 662, 863, 964, 1153, 1351, 1629, 1874, 2244, 2584, 3074, 3507, 4213, 4805, 5725, 6524, 7742, 8770, 10357, 11813, 13936, 15704, 18445, 20896, 24552, 27724

Offset

1,3

Comments

The index of a Lie algebra, g, is an invariant of the Lie algebra defined by min(dim(Ker(B_f)) where the min is taken over all linear functionals f on g and B_f denotes the bilinear form f([_,_]) were [,] denotes the bracket multiplication on g.

For seaweed subalgebras of sl(n), which are Lie subalgebras of sl(n) whose matrix representations are parametrized by an ordered pair of compositions of n, the index can be determined from a corresponding graph called a meander.

a(n)>0 for n>0. To see this for n, take the partition (n).

Links

Table of n, a(n) for n=1..60.

V. Coll, M. Hyatt, C. Magnant, H. Wang, Meander graphs and Frobenius seaweed Lie algebras II, Journal of Generalized Lie Theory and Applications 9 (1) (2015) 227.

V. Dergachev, A. Kirillov, Index of Lie algebras of seaweed type, J. Lie Theory 10 (2) (2000) 331-343.

Crossrefs

Cf. A237832, A318176, A318177, A318178, A318196

Sequence in context: A128976 A199627 A153902 * A046772 A348291 A359652

Adjacent sequences: A318202 A318203 A318204 * A318206 A318207 A318208

Keyword

nonn

Author

Nick Mayers, Aug 21 2018

Status

approved