ABSTRACT

This combinatorics text 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. It presents the computer and software algorithms in pseudo-code and incorporates definitions, theorems, proofs, examples, and nearly 300 illustrations as pedagogical elements of the exposition. Numerous problems, solutions, and hints reinforce basic skills and assist with creative problem solving. The author also offers a website with extensive graph theory informational resources as well as a computational engine to help with calculations for some of the exercises.

chapter Chapter 0|48 pages

Introduction to Combinatorics

chapter Chapter 1|62 pages

Sequences

chapter Chapter 2|50 pages

Solving Recurrences

chapter Chapter 3|56 pages

Evaluating Sums

chapter Chapter 4|41 pages

Binomial Coefficients

chapter Chapter 5|66 pages

Partitions and Permutations

chapter Chapter 6|46 pages

Integer Operators

chapter Chapter 7|60 pages

Graph Fundamentals

chapter Chapter 8|58 pages

Graph Theory Topics

chapter Chapter 9|51 pages

Graph Enumeration

chapter Chapter 10|39 pages

Combinatorial Designs