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## Book Description

This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.

1. Cover
2. Half Title
3. Title Page
5. Contents
6. Preface
7. Chapter 1: Combinatorica: An Explorer’s Guide
1. 1.1 Combinatorial Objects: Permutations, Subsets, Partitions
2. 1.2 Graph Theory and Algorithms
3. 1.3 Combinatorica Conversion Guide
4. 1.4 An Overview of Mathematica
8. Chapter 2: Permutations and Combinations
1. 2.1 Generating Permutations
2. 2.2 Inversions and Inversion Vectors
3. 2.3 Combinations
4. 2.4 Exercises
9. Chapter 3: Algebraic Combinatorics
1. 3.1 The Cycle Structure of Permutations
2. 3.2 Special Classes of Permutations
3. 3.3 Pólya Theory
4. 3.4 Exercises
10. Chapter 4: Partitions, Compositions, and Young Tableaux
1. 4.1 Integer Partitions
2. 4.2 Compositions
3. 4.3 Set Partitions
4. 4.4 Young Tableaux
5. 4.5 Exercises
11. Chapter 5: Graph Representation
1. 5.1 Data Structures for Graphs
2. 5.2 Modifying Graphs
3. 5.3 Classifying Graphs
4. 5.4 Displaying Graphs
5. 5.5 Basic Graph Embeddings
6. 5.6 Improving Embeddings
7. 5.7 Storing and Editing Graphs
8. 5.8 Exercises
12. Chapter 6: Generating Graphs
1. 6.1 Building Graphs from Other Graphs
2. 6.2 Regular Structures
3. 6.3 Trees
4. 6.4 Random Graphs
5. 6.5 Relations and Functional Graphs
6. 6.6 Exercises
13. Chapter 7: Properties of Graphs
1. 7.1 Graph Traversals
2. 7.2 Connectivity
3. 7.3 Cycles in Graphs
4. 7.4 Graph Coloring
5. 7.5 Cliques, Vertex Covers, and Independent Sets
6. 7.6 Exercises
14. Chapter 8: Algorithmic Graph Theory
1. 8.1 Shortest Paths
2. 8.2 Minimum Spanning Trees
3. 8.3 Network Flow
4. 8.4 Matching
5. 8.5 Partial Orders
6. 8.6 Graph Isomorphism
7. 8.7 Planar Graphs
8. 8.8 Exercises
15. Appendix
16. Bibliography
17. Index