Counting and configurations: problems in combinatorics, arithmetic, and geometry

Jiri Herman, Radan Kucera, Jaromir Simsa, K. Dilcher0387955526, 9780387955520

This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. In each topic, brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty, and by exercises that range from routine to rather challenging. While this book emphasizes some methods that are not usually covered in beginning university courses, it nevertheless teaches techniques and skills that are useful not only in the specific topics covered here. There are approximately 310 examples and 650 exercises.
Jiri Herman is the headmaster of a prestigious secondary school (Gymnazium) in Brno, Radan Kucera is Associate Professor of Mathematics at Masaryk University in Brno, and Jaromir Simsa is a researcher at the Mathematical Institute of the Academy of Sciences of the Czech Republic. The translator, Karl Dilcher, is Professor of Mathematics at Dalhousie University in Canada. This book can be seen as a continuation of the previous book by the same authors and also translated by Karl Dilcher, Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory (Springer-Verlag 2000).

---

Table of contents :
Front cover……Page 1
Canadian Mathematical Society……Page 3
CMS Books in Mathematics Series……Page 4
Title page……Page 5
Date-line……Page 6
Preface……Page 7
Contents……Page 11
Symbols……Page 13
1 Combinatorics……Page 15
1 Fundamental Rules……Page 16
2 Standard Concepts……Page 20
3 Problems with Boundary Conditions……Page 38
4 Distributions into Bins……Page 55
5 Proving Identities……Page 69
6 The Inclusion-Exclusion Principle……Page 80
7 Basics of Polya’s Theory of Enumeration……Page 109
8 Recursive Methods……Page 117
2 Combinatorial Arithmetic……Page 121
1 Arrangements……Page 123
2 Sequences……Page 135
3 Arrays……Page 157
4 Unordered Configurations……Page 182
5 Iterations……Page 206
3 Combinatorial Geometry……Page 231
1 Systems of Points and Curves……Page 233
2 Systems of Curves and Regions……Page 255
3 Coverings and Packings……Page 270
4 Colorings……Page 287
1 Hints and Answers to Chapter 1……Page 301
2 Hints and Answers to Chapter 2……Page 325
3 Hints and Answers to Chapter 3……Page 376
Bibliography……Page 399
Index……Page 403
Back cover……Page 407