Combinatorics and Partially Ordered Sets: Dimension Theory
Combinatorics and Partially Ordered Sets: Dimension Theory
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发表时间：
1992-05
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通讯作者：
W. T. Trotter
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作者：
W. T. Trotter
主要是为研究数学家和计算机科学家，组合学和部分有序集：维度理论也作为一个有用的文本为高级学生在任何一个领域。William Trotter专注于有限部分有序集的组合主题，并以维数理论为统一主题，部分有序集或偏序集的研究与组合数学中更传统的主题相关联-包括图论，拉姆齐理论，概率方法，超图，算法和计算几何。本书最重要的贡献是收集、组织和解释了部分有序集上的许多定理，使它们能够被尽可能广泛的读者使用。第3章：次元简介？王冠、分割、堆叠、总和和产品？序集、格、图和集合族的表征问题？超图着色、计算复杂度和不可约偏集？平面poset和树？平面图，平面图和凸多面体？维数论中的概率方法？间隔和几何收容顺序？贪婪维度、回溯和深度优先搜索？有界长度链的乘积？大型最小实现器
Primarily intended for research mathematicians and computer scientists, Combinatorics and Partially Ordered Sets: Dimension Theory also serves as a useful text for advanced students in either field. William Trotter concentrates on combinatorial topics for finite partially ordered sets, and with dimension theory serving as a unifying theme, research on partially ordered sets or posets is linked to more traditional topics in combinatorial mathematics -- including graph theory, Ramsey theory, probabilistic methods, hypergraphs, algorithms, and computational geometry. The book's most important contribution is to collect, organize, and explain the many theorems on partially ordered sets in a way that makes them available to the widest possible audience.Chapters: Introduction to Dimension ? Crowns, Splits, Stacks, Sums and Products ? Characterization Problems for Posets, Lattices, Graphs, and Families of Sets ? Hypergraph Coloring, Computational Complexity, and Irreducible Posets ? Planar Posets and Trees ? Planar Graphs, Planar Maps and Convex Polytopes ? Probabilistic Methods in Dimension Theory ? Interval and Geometric Containment Orders ? Greedy Dimension, Back-Tracking, and Depth First Search ? Products of Chains of Bounded Length ? Large Minimal Realizers