How to count : an introduction to combinatorics / R.B.J.T. Allenby, Alan Slomson.

First published as: an introduction to combinatorics, 1991.

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.

"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."--Publisher's description.