In Section 5, we use the corank function of poset matroids to investigate the relationship between a poset matroid and its dual.

在第5节，我们用偏序集拟阵的余秩函数来研究偏序集拟阵与其对偶之间的关系。

In Section 4, we study the nullity functions of poset matroids.

在第4节研究了偏序集拟阵的零度函数。

An auxiliary relation is an important binary relation on a poset.

辅助关系是定义在偏序集上的一种重要的二元关系.

In this section, we also give a conjecture: A finite lattice is isomorphic to the lattice of flats of a finite poset matroid if and only if it is a semi-modular lattice.

本节的一个中心问题是提出了一个猜想：一个有限格L同构于一个有限偏序集拟阵的闭集所构成的格当且仅当L是一个半模格。

In order to obtain the answers, the applications to study the containment relations between classes of greedoids are discussed by constructing a poset for all greedoids defined on the same set.

为得到答案，首先对于定义在同一集上的全体广义拟阵构造一个偏序关系，运用这种偏序关系讨论不同种的广义拟阵间的包含关系。