Introduction to Enumeration

"I have adopted your text "An introduction to enumeration" for my undergraduate combinatorics course. Overall, it is wonderful...I like how your book actually teaches something, beyond a loose tour of combinatorics that many other books offer. The ability to fluidly go back and forth between recurrences and generating functions, that sort of thing...It trades the broadest focus for specific techniques, in that way reminding me what's fun in say, an ODE course. My students actually learn something they couldn't do before, it makes them feel smart so they like the course " (Prof Dave Bayer, Barnard College, NY, USA)

• What Is Enumeration?.- Generating Functions Count.- Working with Generating Functions.- Permutation Groups.- Matrices, Sequences and Sums.- Group Actions and Counting.- Exponential Generating Functions.- Graphs.- partitions and Paths.

From the reviews: "This work is a very basic, short introduction to combinatorial enumeration techniques. Camina (Univ. of East Anglia, UK) and Lewis (The Mathematical Association, UK) properly explain the fundamental concepts ... . There are 20-25 exercises per chapter ... . The numerical answers to the majority of these exercises are included at the end. ... It may be useful for students who need very basic enumeration skills ... . Summing Up ... . Lower- and upper-division undergraduates." (M. Bona, Choice, Vol. 49 (4), December, 2011) "This book is written as an introduction to enumeration for second or third year undergraduate students in mathematics or computer science. Its theme is counting, using finite or infinite series ... . The development is interspersed with exercises, linked to particular sections, or covering a complete chapter. Solutions are provided at the end of the book." (Andreas N. Philippou, Zentralblatt MATH, Vol. 1230, 2012) "This is an introductory text on counting and combinatorics that has good coverage ... . It is aimed at a sophomore or higher level and has few prerequisites beyond power series. ... There are numerous exercises, and all have brief solutions in the back. ... It is unusual to see a book that combines such extensive coverage with so few prerequisites." (Allen Stenger, The Mathematical Association of America, August, 2011)