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A318238 a(n) is the number of integer partitions of n for which the crank is equal to the index of the seaweed algebra formed by the integer partition paired with its weight. 0
0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 6, 5, 5, 8, 14, 15, 15, 24, 27, 38, 47, 58, 66, 83, 92, 118, 156, 187, 234, 262, 329, 367, 446, 517, 657, 712, 890, 1041, 1270, 1411, 1751, 1951, 2350, 2678, 3278, 3715 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,7
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: if n=k+1 take the partition (k,1).
LINKS
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
Sequence in context: A070610 A156820 A104346 * A341075 A193450 A109906
KEYWORD
nonn,more
AUTHOR
STATUS
approved

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Last modified March 18 22:24 EDT 2024. Contains 370951 sequences. (Running on oeis4.)