Rado's theorem for polymatroids
Rado's theorem for polymatroids
复制标题
多拟阵的拉多定理
DOI：
10.1017/s0305004100051677
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发表时间：
1975
影响因子：
0.8
通讯作者：
C. McDiarmid
中科院分区：
文献类型：
--
作者：
C. McDiarmid
R. Rado（12），其中我提到的名称'Rado的定理拟阵'给出了必要和充分条件的一个家庭的子集的有限集Y有一个横向独立于一个给定的拟阵在Y上。这个定理在截线理论和拟阵理论中都是非常重要的（例如，见（11））。在（3）J埃德蒙兹介绍和研究'polymatroids'作为一种连续模拟的拟阵。我开始这篇论文的简要介绍polymatroids，强调的作用，“地面设置秩函数”。主要结果是一个类似的多拟阵的雷达定理拟阵，我称之为不自然的'雷达定理多拟阵'。
The theorem of R. Rado (12) to which I refer by the name ‘Rado's theorem for matroids’ gives necessary and sufficient conditions for a family of subsets of a finite set Y to have a transversal independent in a given matroid on Y. This theorem is of fundamental importance in both transversal theory and matroid theory (see, for example, (11)). In (3) J. Edmonds introduced and studied ‘polymatroids’ as a sort of continuous analogue of a matroid. I start this paper with a brief introduction to polymatroids, emphasizing the role of the ‘ground-set rank function’. The main result is an analogue for polymatroids of Rado's theorem for matroids, which I call not unnaturally ‘Rado's theorem for polymatroids’.