We show that every gammoid has special digraph representations, such that a representation of the dual of the gammoid may be easily obtained by reversing all arcs. In an informal sense, the duality notion of a poset applied to the digraph of a special representation of a gammoid commutes with the operation of forming the dual of that gammoid. We use these special representations in order to define a complexity measure for gammoids, such that the classes of gammoids with bounded complexity are closed under duality, minors, and direct sums.

中文翻译：

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gammoids 的对偶性表示和兼容的复杂性度量

我们展示了每个 gammoid 都有特殊的有向图表示，这样可以通过反转所有弧来轻松获得 gammoid 对偶的表示。在非正式意义上，应用于 gammoid 的特殊表示的有向图的偏序集的对偶概念与形成该 gammoid 的对偶的操作相交换。我们使用这些特殊表示来定义 gammoids 的复杂性度量，使得具有有限复杂性的 gammoids 类在对偶、次要和直接和下是封闭的。