构形和拟阵的同构映射及关于超可解的几个性质

Isomorphism between arrangements and matroids and some properties of super-solvability

给出了中心超平面构形相交半序集及与其对应的简单拟阵平坦格的同构映射的对应关系,证明了这个映射若限制在模元组成的集合上,也是同构映射,且给出相交半序集和平坦格的模元秩函数之间的关系。另外,还讨论了关于超可解的几个性质。

The one-to-one correspondence between the intersection poset of a central arrangement and the lattice of fiats of a corresponding matroid was given, and ff the above isomorphism restrict on the set of modular elements, then another isomorphism can be obtained. The relationship of the rank function between the intersection poset and the lattice of fiats was provided. In addition, some properties of super-solvability were discussed.