关于广义拟阵间映射的性质  

On the Properties of Maps Between 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,西安710071

出　　处：《天津大学学报（自然科学与工程技术版）》2003年第1期73-77,共5页Journal of Tianjin University：Science and Technology

基　　金：~~

摘　　要：将拟阵间有关强映射和自同构的概念推广到广义拟阵上.给出强映射的判定定理及两种具体找到强映射的方法,为实现用计算机搜寻强映射提供了理论依据.着重讨论区间广义拟阵自同构的判定定理,并推出关于广义拟阵自同构群不存在平坦公理的结论.结果是对在网络和算法上蓬勃发展的广义拟阵理论的充实,为进一步讨论广义拟阵间的关系提供了基础.The concepts of strong map between matroids and an automorphism of a matroid are first extended to that of greedoids,and then followed by presenting some decision theorems for strong maps of greedoids and two methods of finding the strong maps of a greedoid concretely. The methods provide the theoretical foundation for finishing the search of the concrete strong maps of a greeedoid with computer. Thirdly, discussions about the automorphism group of an interval greedoid are made and two decision theorems about it are established. As a consequence,a flat axiom is found that it is not existed in the automorphism group of a greedoid. All the results described in this paper a complementary to the greedoid theory which is developing in network and greedy algorithm vigorously. Moreover, they provide a basis for the study on the relationships between greedoids.

关 键 词：平坦集 广义拟阵 强映射 自同构 判定定理 偏序集 组合结构 

分 类 号：O153.1[理学—数学] O157[理学—基础数学]