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Foreword
Preface
Acknowledgement

I Basic Methods
Ch. 1 Seven Is More Than Six. The Pigeon-Hole Principle 1
Ch. 2 One Step at a Time. The Method of Mathematical Induction 19

II Enumerative Combinatorics
Ch. 3 There Are A Lot Of Them. Elementary Counting Problems 37
Ch. 4 No Matter How You Slice It. The Binomial Theorem and Related Identities 65
Ch. 5 Divide and Conquer. Partitions 89
Ch. 6 Not So Vicious Cycles. Cycles in Permutations 109
Ch. 7 You Shall Not Overcount. The Sieve 131
Ch. 8 A Function Is Worth Many Numbers. Generating Functions 145

III Graph Theory
Ch. 9 Dots and Lines. The Origins of Graph Theory 183
Ch. 10 Staying Connected. Trees 207
Ch. 11 Finding A Good Match. Coloring and Matching 239
Ch. 12 Do Not Cross. Planar Graphs 265

IV Horizons
Ch. 13 Does It Clique? Ramsey Theory 283
Ch. 14 So Hard To Avoid. Subsequence Conditions on Permutations 301
Ch. 15 Who Knows What It Looks Like, But It Exists. The Probabilistic Method 339
Ch. 16 At Least Some Order. Partial Orders and Lattices 369

Bibliography 401
Index 403

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.

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.