偏序集拟阵与广义拟阵的关系  

Relations between poset matroids and greedoids

作　　者：毛华[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学数学系,陕西西安710071

出　　处：《陕西师范大学学报（自然科学版）》2003年第1期1-3,共3页Journal of Shaanxi Normal University：Natural Science Edition

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：研究了偏序集拟阵与广义拟阵的关系.利用偏序集拟阵秩闭包算子的性质与广义拟阵闭包算子性质的比较得出:偏序集拟阵为广义拟阵;通过广义拟阵自同构群的公理系统与偏序集拟阵相应性质的比较得出:广义拟阵不一定为偏序集拟阵.This paper deals with the relations between poset matroids and greedoids. The first is to show that any poset matroid is a greedoid by comparing the property of rank closure operator of poset matroids with the relative property of closure operator of greedoids. In addition, by comparing the axioms of automorphism group of greedoids with that of poset matroids, it is proved that a greedoid is not necessary a poset matroid.

关 键 词：偏序集拟阵 秩闭包算子 广义拟阵 自同构群 对偶理想 有限集 互为支撑公理 

分 类 号：O157.5[理学—数学]