Combinatorial Methods with Computer Applications

PUBLISHER’S DESCRIPTION

• Provides a thorough, up-to-date treatment of combinatorics that covers topics such as asymptotics, graphs, and evaluating sums
• Presents the computer algorithms in easy-to-read pseudo-code
• Foreshadows difficult topics early in the book to prepare students for more in-depth discussions later on
• Incorporates definitions, theorems, proofs, examples, and nearly 300 illustrations as pedagogical elements of the exposition
• Includes numerous problems, along with many solutions and hints, that range from the reinforcement of basic skills to creative problem solving
• Offers a companion website that contains extensive graph theory informational resources as well as a computational engine to help with calculations for some of the exercises

Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course.

After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces.

Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.