The dimension of the maximal parabolic seaweed algebra corresponding to the partition. Let $a_1,\dots,a_m$ and $b_1,\dots,b_t$ be two compositions of $n$. The corresponding seaweed algebra is the associative subalgebra of the algebra of $n\times n$ matrices which preserves the flags $$ \{0\} \subset V_1 \subset \cdots \subset V_{m-1} \subset V_m =V $$ and $$ V=W_0\supset W_1\supset \cdots \supset W_t=\{0\}, $$ where $V_i=\text{span}\{e_1,\dots, e_{a_1+\cdots +a_i}\}$ and $W_j=\text{span}\{e_{b_1+\cdots +b_j+1},\dots, e_n\}$. Thus, its dimension is $$ \frac{1}{2}\left(\sum a_i^2 + \sum b_i^2\right). $$ It is maximal parabolic if $b_1=n$.