Introduction to Combinatorics (Discrete Mathematics and Its Applications)

Introduction to Combinatorics by Walter D. Wallis and John C. George provides a comprehensive introduction to the branch of mathematics dealing with different ways of selecting objects from a set or arranging them. This text explores two major types of questions: counting questions, which involve determining the number of ways a selection or arrangement can be chosen with specific properties, and structural questions, which seek to identify whether a particular selection or arrangement exists with specific properties. The book covers various topics, including enumerative ideas, probability, generating functions, and recurrences, as well as important families of functions and numbers. It also delves into computer algebra, group theory, posets, graphs, codes, Latin squares, and experimental designs. The authors' goal is to provide a thorough focus on accuracy, with numerous illustrations, exercises, and problems. The book includes two new chapters on probability and posets, as well as appendices covering sets, induction and proof techniques, vectors and matrices, and biographies with historical notes. It also features flexible use of MapleTM and MathematicaTM to aid in understanding and applying combinatorial concepts.