Computational Discrete Mathematics Combinatorics and Graph Theory with Mathematica ®

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. Combinatorica: an explorer's guide; 2. Permutations and combinations; 3. Algebraic combinatorics; 4. Partitions, compositions and Young tableaux; 5. Graph representation; 6. Generating graphs; 7. Properties of graphs; 8. Algorithmic graph theory.

Steven Skiena is Distinguished Teaching Professor of Computer Science at Stony Brook University. His research interests include the design of graph, string, and geometric algorithms, and their applications (particularly to biology). He is the author of five books, including The Algorithm Design Manual and Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win. He is co-founder and Chief Scientist at General Sentiment (www.generalsentiment.com), a media measurement company based on his Lydia text/sentiment analysis system. Skiena received his PhD in Computer Science from the University of Illinois in 1988, and is the author of over 130 technical papers. He is a former Fulbright scholar, and a recipient of the ONR Young Investigator Award and the IEEE Computer Science and Engineer Teaching Award.