

A318196


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


6



0, 0, 1, 1, 2, 2, 5, 4, 7, 7, 16, 11, 23, 22, 43, 41, 61, 56, 97, 103, 126, 146, 205, 210, 274, 315, 389, 461, 531, 623, 751, 901, 968, 1227, 1372, 1661, 1787, 2238, 2332, 2998, 3105, 3921, 4103, 5241, 5148, 6778, 6795, 8745, 8683, 11231, 11133, 14523, 14246, 18284, 18121, 23536, 22790, 29627, 29143, 36990
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OFFSET

1,5


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>2. To see this: for n odd, say n=2k+3, take the partition (2k+1,1,1); for n even, say n=2k+4, take the partition (2k+1,1,1,1).


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) 331343.


CROSSREFS

Cf. A237832, A318176, A318177, A318178, A318203
Sequence in context: A162200 A290289 A000019 * A081177 A007281 A101085
Adjacent sequences: A318193 A318194 A318195 * A318197 A318198 A318199


KEYWORD

nonn


AUTHOR

Nick Mayers, Aug 20 2018


STATUS

approved



