子偏序集拟阵  

Subposetmatroids

作　　者：毛华[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学理学院,陕西西安710071

出　　处：《西安电子科技大学学报》2002年第6期796-799,808,共5页Journal of Xidian University

基　　金：国家自然科学基金资助项目(69972036);陕西省自然科学基金资助项目(2000SL03)

摘　　要：文中利用偏序集理论将拟阵理论研究中扮演重要角色的"子"运算(截短、延长、约束和收缩)引入新理论中,并首次提出了偏序集拟阵连通的概念.此外,利用"子"运算给出了判定偏序集拟阵是否连通的方法;讨论了偏序集拟阵与另一种常见拟阵理论的推广———广义拟阵的关系,特别讨论了偏序集拟阵与反拟阵的关系.为深入探讨偏序集理论提供了一种新思路.This paper first extends 'sub' operations of matroids (truncation, elongation, restriction and contraction) to poset matroids by dint of the poset theory and gives the concept of poset matroid connection for the first time. Then, a decision method for poset matroid connection is obtained by means of 'sub' operations of poset matroids. After that, using 'sub' operations, the relations between poset matroids and greedoids (another common generalization of matroids), especially antimatroids are discussed. And furthermore, the 'sub' method for discussing the relations between poset matroids and antimatroids appears. This paper gives a new idea for investigating further into poset matroids.

关 键 词：偏序集拟阵 子偏序集拟阵 连通拟阵 广义拟阵 

分 类 号：O157[理学—数学] O153.1[理学—基础数学]