Lectures on discrete geometry
Lectures on discrete geometry
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DOI：
10.1007/978-1-4613-0039-7
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发表时间：
2002-05
期刊：
影响因子：
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通讯作者：
J. Matoušek
中科院分区：
文献类型：
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作者：
J. Matoušek
这本书主要是一本介绍离散几何各个领域的教科书。在每个领域，它以一种易于理解和具体的方式解释了几个关键的结果和方法。它还在单独的部分中包含更高级的材料，因此它可以作为几个较窄子领域的调查集合。主要内容包括：凸集、凸多面体和超平面排列的基础知识；几何构型的组合复杂度；凸集的相交模式与截线；几何ramsey型结果；多面体组合与高维凸性；最后，将有限度量空间嵌入赋范空间。
This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces.