拟阵之间的弱映射与秩弱映射

Weak maps and rank-weak maps between matroids

鉴于Welsh给出的拟阵弱映射与强映射关系不太自然,重新定义了拟阵之间的弱映射,并引入了秩弱映射和反射独立集的映射的概念.这就使得强映射总是弱映射,而且一个映射是秩弱映射当且仅当其扩张是弱映射.讨论了秩弱映射、反射独立集的映射以及反射闭集的映射之间的关系,利用这些映射给出了拟阵同构的等价刻画,说明了弱映射和秩弱映射也是合适的拟阵态射.

Concerning that the relation between Welsh＇s weak maps and strong maps is not very good, a new definition of weak map is given and the concepts of rank-weak maps and independent setsreflected maps are introduced. Thus a strong map must be weak and a map is rank-weak if and only if its extension is! weak. Then the relations among rank-weak maps, independent set-reflected maps and closed set-reflected are studied. The isomorphism between matroids is characterized by these new maps, which shows that both weak map and rank-weak map are appropriate morphisms for matroids.