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Computational discrete mathematics. Combinatorics and graph theory with Mathematica. (English) Zbl 1067.05001
Cambridge: Cambridge University Press (ISBN 0-521-80686-0/hbk). xiv, 480 p. (2003).
This book is a complete revision of the original description of the package Combinatorica (an extension of Mathematica), S. Skiena [Implementing discrete mathematics. Combinatorics and graph theory with Mathematica (Addison–Wesley, Redwood City, CA) (1990; Zbl 0786.05004)]. It provides a definitive user’s guide to Combinatorica, which itself has been rewritten. The book covers two pillars of discrete mathematics, classical combinatorics and graph theory. On the side of combinatorics, the main concern is generating combinatorial objects, like permutations, combinations, partitions, Young tableaux. The approach to graph theory is, of course, algorithmic. The book does not assume familiarity of the reader with discrete mathematics, and can be used as a computer-assisted introduction into this field. Using this book can be a good way to teach discrete mathematics for computer science majors. Another possible use is to provide illustration in the classroom to concepts and results of discrete mathematics, or, for more advanced users, testing conjectures on small examples. The titles of the chapters of the book give more information on the topics covered: 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.

05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics
05-04 Software, source code, etc. for problems pertaining to combinatorics
68R05 Combinatorics in computer science
68W05 Nonnumerical algorithms
68W30 Symbolic computation and algebraic computation
Zbl 0786.05004