Table of Contents

IN ONE LINE AND CLOSE. PERMUTATIONS AS LINEAR ORDERS. RUNS
Descents
Alternating Runs
IN ONE LINE AND ANYWHERE. PERMUTATIONS AS LINEAR ORDERS. INVERSIONS
Inversions
Inversion in Permutations of Multisets
IN MANY CIRCLES: PERMUTATIONS AS PRODUCTS OF CYCLES
Decomposing a Permutation into Cycles
Type and Stirling Numbers
Cycle Decomposition versus Linear Order
Permutations with Restricted Cycle Structure
IN ANY WAY BUT THIS: PATTERN AVOIDANCE; THE BASICS
The Notion of Pattern Avoidance
Patterns of Length Three
Monotone Patterns
Patterns of Length Four
The Proof of the Stanley-Wilf Conjecture
IN THIS WAY, BUT NICELY: PATTERN AVOIDANCE; THE FOLLOW-UP
Polynomial Recursions
Containing a Pattern Many Times
Containing a Pattern a Given Number of Times
MEAN AND INSENSITIVE: RANDOM PERMUTATIONS
The Probabilistic Viewpoint
Expectation
Variance and Standard Deviation
An Application: Longest Increasing Subsequences
PERMUTATIONS vs. EVERYTHING ELSE: ALGEBRAIC COMBINATORICS OF PERMUTATIONS
The Robinson-Schensted-Knuth Correspondence
Posets of Permutations
Simplicial Complexes of Permutations
GET THEM ALL: ALGORITHMS AND PERMUTATIONS
Generating Permutations
Stack Sorting Permutations
Variations of Stack Sorting
SOLUTIONS TO ODD-NUMBERED EXERCISES
REFERENCES
LIST OF FREQUENTLY USED NOTATIONS
INDEX

Each chapter also includes Exercises, Problems Plus, and Solutions to Problems Plus sections

Reviews

"We found the author’s explanations very clear, and there is an abundance of useful examples and helpful figures . . . There is a rich bibliography for those seeking more information or full proofs of cited results." – R. Gregory Taylor, in SIGACT News, October 2008 "[This book] was written by the author with love and enthusiasm for the subject and is a pleasure to read. Undergraduate and graduate students in combinatorics, as well as researchers, will find in it many interesting results and inspiring questions."
- Mathematical Reviews, 2005f

"The literature on permutations is as extensive as permutations are manifold. … What was missing until now was a comprehensive up-to-date treatment to all aspects of the combinatorics of permutations. The author [of this book] has written it. … This is the first book which gives a systematic introduction to this fascinating and active area of research. … All the subjects are presented in a very pleasant way: developments are always well motivated, explanations are transparent and illustrated by numerous examples. At the end of each chapter the reader finds a list of exercises, with detailed solutions … [containing] references [that] … are excellent starting points for further research."
- Zentralblatt für Mathematik


"One can easily imagine gems from this book forming the basis of a Martin Gardner-type column. … [T]he fascinating chapters here on pattern avoidance, particularly the formulation and proof of the Stanley-Wilf and Furedi-Hajnal conjectures, make this book essential. … The author shows himself the master expositor, always efficient while never terse, ever the clairvoyant and generous anticipator of misreadings that might trip readers. Summing Up: Essential."
- CHOICE


"Until now it was necessary to consult a myriad of sources, from textbooks to journal articles, in order to grasp the whole picture. Now, however, Miklós Bóna has provided us with a comprehensive, engaging, and eminently readable introduction to all aspects of the combinatorics of permutations…

"This book can be utilized at a variety of levels, from random samplings of the treasures therein to a comprehensive attempt to master all the material and solve all the exercises. In whatever direction the reader's tastes lead, a thorough enjoyment and appreciation of a beautiful area of combinatorics is certain to ensue."
- From the Foreword by Richard Stanley

"This book aims to round up any topic related to the combinatorial nature of permutations and present it between one set of covers…Throughout the book, there are frequent references to the excellent bibliography of more than two hundred research articles and books. It is clear that the author finds his topic to be full of 'serious fun.' This enthusiasm is conveyed in the conversational and engaging style of the writing…This book was written to be used in a graduate-level topics course. For that purpose it is ideally suited…Experienced researchers in combinatorics will find the book useful as a guide to the literature on permutations. For graduate students with advanced interests in any field of combinatorics, the faculty who work with these students, or the libraries that support them, this book is an excellent choice."
-SIAM Review