## Counting and Configurations: Problems in Combinatorics, Arithmetic, and GeometryThis book can be seen as a continuation of Equations and Inequalities: El ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series. How ever, it can be independently read or used as a textbook in its own right. This book is intended as a text for a problem-solving course at the first or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with combinatorics, graph theory, number theory, or geometry, or for any of the discrete mathematics courses that are offered at most American and Canadian universities. The underlying "philosophy" of this book is the same as that of Equations and Inequalities. The following paragraphs are therefore taken from the preface of that book. |

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### Contents

Combinatorics | 1 |

1 Fundamental Rules | 2 |

2 Standard Concepts | 6 |

3 Problems with Boundary Conditions | 24 |

4 Distributions into Bins | 41 |

5 Proving Identities | 55 |

6 The InclusionExclusion Principle | 66 |

7 Basics of Polyas Theory of Enumeration | 95 |

4 Unordered Configurations | 168 |

5 Iterations | 192 |

Combinatorial Geometry | 217 |

1 Systems of Points and Curves | 219 |

2 Systems of Curves and Regions | 241 |

3 Coverings and Packings | 256 |

4 Colorings | 273 |

Hints and Answers | 287 |

8 Recursive Methods | 103 |

Combinatorial Arithmetic | 107 |

1 Arrangements | 109 |

2 Sequences | 121 |

3 Arrays | 143 |

2 Hints and Answers to Chapter 2 | 311 |

3 Hints and Answers to Chapter 3 | 362 |

385 | |

389 | |

### Other editions - View all

Counting and Configurations: Problems in Combinatorics, Arithmetic, and Geometry Jiri Herman,Radan Kucera,Jaromir Simsa No preview available - 2013 |

Counting and Configurations: Problems in Combinatorics, Arithmetic, and Geometry Jiri Herman,Radan Kucera,Jaromir Simsa No preview available - 2010 |

### Common terms and phrases

anagrams arbitrary arithmetic sequence arrangement assertion assume bijection binomial coefficients bins Burnside's lemma chessboard choose chosen circle classes color column consider contradiction convex polygon denote the number desired number desired property determine the number diagonals digit sum digits disk distinct distributions divided equal equation Exercises fc-element fields Figure Find the number finite follows geometric sequence given Hence holds identity implies inclusion-exclusion principle inequality intersections largest least line segment multiplication rule multiset n x n array n-element set n-tuple neighboring nonempty number n number of elements number of solutions obtain pairs partition pigeonhole principle plane polygon positive integers possible problems proof real numbers recurrence relation regions relatively prime remaining respectively satisfies Section sequence of length Show side length smallest square subarray subsets summands Suppose total number transformation triangle triple vertices