Transforms, Diagrams and Representations
Transforms, Diagrams and Representations
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变换、图表和表示
DOI：
10.1007/978-3-0348-5765-9_4
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发表时间：
1979
期刊：
影响因子：
--
通讯作者：
P. McMullen
中科院分区：
文献类型：
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作者：
P. McMullen
近年来，凸性组合理论中的一些更引人注目的进展来自于各种图表技术。事后看来，我们可以将该理论的起源追溯到 Whitney [1935]，这篇论文也引发了拟阵的卓有成效的研究（另见下面的 8A）。然而，目前设想的想法首先以可识别的形式出现在 Gale [1956] 中，尽管相关的想法出现在 Motzkin [1951] 和 Davis [1954] 中。该主题目前的发展主要归功于 Perles（他的工作在 Grünbaum [1967] 中有描述），以及后来 McMullen 和 Shephard 的一系列论文（稍后将在适当的地方给出参考文献）。
A number of the more striking advances in the combinatorial theory of convexity in recent years have come from the various kinds of diagram techniques. With benefit of hindsight, we can trace the origins of the theory to Whitney [1935], a paper which also initiated the fruitful study of matroids (see also 8A below). However, the idea as presently envisaged first appears in a recognizable form in Gale [1956], though related ideas appear in Motzkin [1951] and Davis [1954]. The present development of the subject is due largely to Perles (whose work is described in Grünbaum [1967]) and, later, to a series of papers by McMullen and Shephard (references will be given later, in the appropriate places).