Abstract Analogous to the types A, B, and C cases, we address the computation of the index of seaweed subalgebras in the type-D case. Formulas for the algebra’s index can be computed by counting the connected components of its associated meander. We focus on a set of distinguished vertices of the meander, called the tail of the meander, and using the tail, we provide comprehensive combinatorial formulas for the index of a seaweed in all the classical types. Using these formulas, we provide all general closed-form index formulas where the index is given by a polynomial greatest common divisor formula in the sizes of the parts that define the seaweed.

中文翻译：

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海藻类李代数的组合指数公式

摘要 类似于 A、B 和 C 类情况，我们解决了 D 类情况下海藻子代数指数的计算。代数指数的公式可以通过计算其相关曲折的连通分量来计算。我们专注于一组著名的曲折顶点，称为曲折的尾巴，并使用尾巴，我们提供了所有经典类型海藻指数的综合组合公式。使用这些公式，我们提供了所有一般封闭式指数公式，其中指数由定义海藻的部分大小的多项式最大公约数公式给出。