Combinatorial Order Theory
Combinatorial Order Theory
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DOI：
10.1007/978-1-4615-6666-3_9
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发表时间：
1979
期刊：
影响因子：
--
通讯作者：
M. Aigner
中科院分区：
文献类型：
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作者：
M. Aigner
在一般术语“组合序理论”下，我们希望收集一些关于偏序集的结果，而不是关注偏序集的结构，而是关注任何偏序集中存在的性质，如链、反链、匹配等。要考虑的典型问题是确定有限偏序集可以分解成的最小链数或秩偏序集的点与点之间是否存在匹配。事实上，这个组合数学分支的重要性在很大程度上源于这样一个事实，即大多数主要结果是存在性定理，补充了第三章到第五章中建立的许多计数结果。为了证明其广泛的应用范围，我们包括了来自不同来源的各种例子（图，网络，0,1-矩阵等）。每个部分都以一个基本定理为开头，之后我们研究主要定理的变化、应用以及与其他结果的相互依赖性。
Under the general term “combinatorial order theory” we want to collect some results on posets by concentrating less on the structure of posets than on properties present in any poset, such as chains, antichains, matchings, etc. Typical problems to be considered are the determination of the minimal number of chains into which a finite poset can be decomposed or the existence of a matching between the points and copoints of a ranked poset. In fact, the importance of this branch of combinatorial mathematics derives to a large extent from the fact that most of the main results areexistence theoremssupplementing the many counting results established in chapters III to V. To testify to the broad range of applications, we have included a variety of examples from different sources (graphs, networks, 0,1-matrices, etc.). Each of the sections is headed by a basic theorem after which we study variations of the main theorem, applications, and the mutual dependence with other results.