cp's OEIS Frontend

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.

%I A318205 #7 Sep 19 2018 06:18:10
%S A318205 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,
%T A318205 135,162,209,243,300,350,425,484,600,662,863,964,1153,1351,1629,1874,
%U A318205 2244,2584,3074,3507,4213,4805,5725,6524,7742,8770,10357,11813,13936,15704,18445,20896,24552,27724
%N 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.
%C A318205 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 A318205 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 A318205 a(n)>0 for n>0. To see this for n, take the partition (n).
%H A318205 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 A318205 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 A318205 Cf. A237832, A318176, A318177, A318178, A318196
%K A318205 nonn
%O A318205 1,3
%A A318205 _Nick Mayers_, Aug 21 2018