Analogous to the 𝔰𝔩 (n) case, we address the computation of the index of seaweed
subalgebras of 𝔰𝔭 (2 n) by introducing graphical representations called symplectic …

The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to
compute. However, for the suggestively-named seaweed algebras, the computation of the …

If gg is a Frobenius Lie algebra, then for certain F ∈ g^* F∈ g∗ the natural map g ⟶ g^* g⟶
g∗ given by x ⟼ F x,-x⟼ F x,-is an isomorphism. The inverse image of F under this …

arXiv:1809.09271v2 [math.CO] 9 Oct 2018 Page 1 arXiv:1809.09271v2 [math.CO] 9 Oct 2018
Statistics on integer partitions arising from seaweed algebras Vincent E. Coll, Jr.*, Andrew W …

By using a free monoid of operators on the set of compositions (resp. pairs of compositions),
we establish in this paper a bijective correspondence between Frobenius standard …

Closed meanders are planar configurations of one or several disjoint closed Jordan curves
intersecting a given line or curve transversely. They arise as shooting curves of parabolic …

This unique book's subject is meanders (connected, oriented, non-self-intersecting planar
curves intersecting the horizontal line transversely) in the context of dynamical systems. By …

Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic
zero. We provide necessary and also some sufficient conditions in order for its Poisson …

Analogous to the Type-$ A_ {n-1}=\mathfrak {sl}(n) $ case, we show that if $\mathfrak {g} $ is
a Frobenius seaweed subalgebra of $ B_ {n}=\mathfrak {so}(2n+ 1) $ or $ C_ {n}=\mathfrak …

The index of a Lie algebra g is defined by ind g= min f∈ g* dim (ker (B f)), where f is an
element of the linear dual g* and B f (x, y)= f ([x, y]) is the associated skew-symmetric Kirillov …