Allenby R.B.J.T., SlomsonA. How to Count. An Introduction to Combinatorics

Chapman & Hall/CRC Press, 2011. — 440 p.Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics.
This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises.
Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.What’s It All About?
Permutations and Combinations
Occupancy Problems
The Inclusion–Exclusion Principle
Stirling and Catalan Numbers
Partitions and Dot Diagrams
Generating Functions and Recurrence Relations
Partitions and Generating Functions
Introduction to Graphs
Trees
Groups of Permutations
Group Actions
Counting Patterns
Pólya Counting
Dirichlet’s Pigeonhole Principle
Ramsey Theory
Rook Polynomials and Matchings