A Course in Topological Combinatorics

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Springer Science & Business Media, Jun 30, 2012 - Mathematics - 240 pages
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A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, and other applied areas. Topological combinatorics is concerned with solutions to combinatorial problems by applying topological tools. In most cases these solutions are very elegant and the connection between combinatorics and topology often arises as an unexpected surprise.

The textbook covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. The text contains a large number of figures that support the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given, and each chapter ends with a series of exercises. The extensive appendix makes the book completely self-contained.

The textbook is well suited for advanced undergraduate or beginning graduate mathematics students. Previous knowledge in topology or graph theory is helpful but not necessary. The text may be used as a basis for a one- or two-semester course as well as a supplementary text for a topology or combinatorics class.

 

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Contents

Chapter 1 FairDivision Problems
1
Chapter 2 GraphColoring Problems
37
Chapter 3 Evasiveness of Graph Properties
69
Chapter 4 Embedding and Mapping Problems
96
Chapter 5 Appendix A Basic Concepts from Graph Theory
145
Chapter 6 Appendix B Crash Course in Topology
163
Chapter 7 Appendix C Partially Ordered Sets Order Complexes and Their Topology
198
Chapter 8 Appendix D Groups and Group Actions
209
Chapter 9 Appendix E Some Results and Applications from Smith Theory
219
References
229
Index
233
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About the author (2012)

Mark de Longueville is professor of Mathematics at Hochschule für Technik und Wirtschaft Berlin and faculty member of the Berlin branch of New York University.

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