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These typically include, but are not limited to, the easiest exercises in that chapter. A solution manual for the Supplementary Exercises is available for Instructors. I am certainly indebted to the books I used in my teaching during this time. Several exercises in the book come from my long history as a student mathematics competition participant.
I am grateful to my students who never stopped asking questions and showed which part of the material needed further explanation. Some of the presented material was part of my own research, sometimes in collaboration. I am also indebted to my former advisor, Richard Stanley, who introduced me to the fascinating area of Pattern Avoidance, discussed in Chapter My gratitude is extended to Joseph Sciacca for the cover page.
After the publication of the first edition in , several mathematicians contributed lists of typographical errors to be corrected. I am thankful for their help in making the second edition better by communicating those lists to me, as well as for similar help from countless other contributors who will hopefully forgive that I do not list all of them here.
Most of the corrections for the second edition were provided by Margaret Bayer, and for the third edition by Glenn Tesler. Most of all, I must thank my wife Linda, my first reader, who made it possible for me to spend long hours writing this book while she also had her hands full.
See Exercise 3 of Chapter 15 for further explanation. Basic Methods 1. Seven Is More Than Six. The Pigeon-Hole Principle 1. Supplementary Exercises. Solutions to Exercises. One Step at a Time. The Method of Mathematical Induction 2. Supplementary Exercises Solutions to Exercises. Enumerative Combinatorics 3. Elementary Counting Problems 3.
Strings over a Finite Alphabet. The Binomial Theorem and Related Identities 4. Divide and Conquer. Partitions 5. Not So Vicious Cycles. Cycles in Permutations 6. Chegg Solution Manuals are written by vetted Chegg Math experts, and rated by students - so you know you're getting high quality answers.
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