| Physical description |
xvii, 406 pages : illustrations ; 24 cm |
| Bibliography |
Includes bibliographical references (pages 401-402) and index. |
| Contents |
I. Basic Methods -- Ch. 1. Seven Is More Than Six. The Pigeon-Hole Principle -- Ch. 2. One Step at a Time. The Method of Mathematical Induction -- II. Enumerative Combinatorics -- Ch. 3. There Are A Lot Of Them. Elementary Counting Problems -- Ch. 4. No Matter How You Slice It. The Binomial Theorem and Related Identities -- Ch. 5. Divide and Conquer. Partitions -- Ch. 6. Not So Vicious Cycles. Cycles in Permutations -- Ch. 7. You Shall Not Overcount. The Sieve -- Ch. 8. A Function Is Worth Many Numbers. Generating Functions -- III. Graph Theory -- Ch. 9. Dots and Lines. The Origins of Graph Theory -- Ch. 10. Staying Connected. Trees -- Ch. 11. Finding A Good Match. Coloring and Matching -- Ch. 12. Do Not Cross. Planar Graphs -- IV. Horizons -- Ch. 13. Does It Clique? Ramsey Theory -- Ch. 14. So Hard To Avoid. Subsequence Conditions on Permutations -- Ch. 15. Who Knows What It Looks Like, But It Exists. The Probabilistic Method. |
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Ch. 16. At Least Some Order. Partial Orders and Lattices. |
| Summary |
This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication, " is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course. |
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It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and -- probably the first of its kind -- pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading. |
| Subject |
Combinatorial analysis.
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| ISBN |
9810249004 (alkaline paper) |
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