Matroids as the Study of Geometrical Configurations
Matroids as the Study of Geometrical Configurations
复制标题
拟阵作为几何构型的研究
DOI：
10.1007/978-94-010-1220-1_9
复制
发表时间：
1977
期刊：
影响因子：
--
通讯作者：
J. H. Mason
中科院分区：
文献类型：
--
作者：
J. H. Mason
拟阵出现在各种组合和代数环境中。的想法
向量空间中的独立性和基数
代数依赖中的依赖
电路如图所示
射影几何中的平面
原子半模晶格，
所有这些都归结为相同的基础结构。拟阵的基本特征是它们从某种情况中提取与几何相关的点、线和平面的基本关联属性。它们出现在如此多的地方并进行伪装，这表明它们是值得研究的对象。研究的开展方式在某种程度上受到方法方向的影响。图论提出了某些可以推广的思想，格论提出了其他思想，向量空间还提出了其他思想。通常，几何方面似乎被大量的代数符号迷失了。
Matroids arise in a variety of combinatorial and algebraic contexts. The ideas of
independence and bases as in vector spaces
dependence as in algebraic dependence
circuits as in graphs
flats as in projective geometries
atomic semimodular lattices,
all come down to the same underlying structure. The essential feature of matroids is that they extract from a situation the basic incidence properties of points, lines and planes which we associate with geometry. That they show up in so many places and disguises suggests them as worthwhile objects of study. How that study is carried out is affected to some extent by the direction of approach. Graph theory suggests certain ideas to be generalised, lattice theory suggests others, and vector spaces still others. Often it seems that the geometrical aspect is lost in a profusion of algebraic notation.