On the Maps Between Antimatroids

In this paper, the definitions of the most common and elementary mappings between matroids are extended to antimatroids first. Then the poset theory is used to find out the fiats of an antimatroid and obtain all of strong maps for a given antimatroid. Besides, the poset theory is also used to deal with the relationships among the mappings between antimatroids. All the discussion is connected with poset theory. This claims that poset theory is an important tool for the study of antimatroid theory.

反拟阵、凸几何与伽罗瓦连接的关系及其应用

通过揭示凸几何与由对象集和属性集组成的信息系统的伽罗瓦连接之间的对应关系,得到信息分类的反拟阵和凸几何方法,并将其应用于生物分类中。首先在一个信息集合组成的凸几何上,以构造方式得到两种不同信息系统的伽罗瓦连接;其次得到由一个信息系统的伽罗瓦连接产生唯一凸几何的条件,再分别得到利用反拟阵和凸几何方法进行信息提取的思路;最后利用上述方法对一个生物信息系统实例进行了成功的分类。

反拟阵自同构群的公理系统及其性质

给出了反拟阵自同构群的定义,利用反拟阵的公理系统建立其自同构群公理系统;在此基础上,讨论了拟阵与反反拟阵之间的一些关系。