cp's OEIS Frontend

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.

%I A318238 #9 Sep 19 2018 06:18:23
%S A318238 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,
%T A318238 187,234,262,329,367,446,517,657,712,890,1041,1270,1411,1751,1951,
%U A318238 2350,2678,3278,3715
%N 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.
%C A318238 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.
%C A318238 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.
%C A318238 a(n)>0 for n>2. To see this: if n=k+1 take the partition (k,1).
%H A318238 V. Coll, M. Hyatt, C. Magnant, H. Wang, <a href="http://dx.doi.org/10.4172/1736-4337.1000227">Meander graphs and Frobenius seaweed Lie algebras II</a>, Journal of Generalized Lie Theory and Applications 9 (1) (2015) 227.
%H A318238 V. Dergachev, A. Kirillov, <a href="https://www.emis.de/journals/JLT/vol.10_no.2/6.html">Index of Lie algebras of seaweed type</a>, J. Lie Theory 10 (2) (2000) 331-343.
%Y A318238 Cf. A237832, A318176, A318177, A318178, A318196, A318203
%K A318238 nonn,more
%O A318238 1,7
%A A318238 _Nick Mayers_, _Melissa Mayers_, Aug 21 2018