cp's OEIS Frontend

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.

%I A318196 #10 Sep 19 2018 06:17:47
%S A318196 0,0,1,1,2,2,5,4,7,7,16,11,23,22,43,41,61,56,97,103,126,146,205,210,
%T A318196 274,315,389,461,531,623,751,901,968,1227,1372,1661,1787,2238,2332,
%U A318196 2998,3105,3921,4103,5241,5148,6778,6795,8745,8683,11231,11133,14523,14246,18284,18121,23536,22790,29627,29143,36990
%N 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.
%C A318196 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 A318196 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 A318196 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).
%H A318196 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 A318196 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 A318196 Cf. A237832, A318176, A318177, A318178, A318203
%K A318196 nonn
%O A318196 1,5
%A A318196 _Nick Mayers_, Aug 20 2018