A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory

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World Scientific, 2006 - Mathematics - 469 pages
2 Reviews
This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. 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.
 

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superb book.....................

Contents

Basic Methods
1
One Step at a Time The Method of Mathematical Induction
19
Enumerative Combinatorics
37
No Matter How You Slice It The Binomial Theorem
65
Divide and Conquer Partitions
89
Not So Vicious Cycles Cycles in Permutations
109
You Shall Not Overcount The Sieve
131
Functions
164
Do Not Cross Planar Graphs
269
Horizons
287
So Hard To Avoid Subsequence Conditions on Permutations
307
Who Knows What It Looks Like But It Exists
345
Exercises
363
At Least Some Order Partial Orders and Lattices
375
The Sooner The Better Combinatorial Algorithms
407
Does Many Mean More Than One? Computational Complexity
433

Graph Theory
183
Staying Connected Trees
209
Finding A Good Match Coloring and Matching
241

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