See our review of the first edition. The combinatorics of permutations remains an active topic of research, and the last eight years have brought many new results. As a result, says the author, the new edition required "some painful choices as to what to include." There is a new chapter nine, "devoted to sorting algorithms whose original motivation comes from molecular biology." Chapters 1, 3, 4, and 6 have been "significantly changed and expanded" and all chapters have new exercises and problems, some of which reflect recent results.
This is an excellent book on an important subject.
In One Line and Close. Permutations as Linear Orders.
In One Line and Anywhere. Permutations as Linear Orders. 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
Patterns of Length Four
The Proof of the Stanley–Wilf Conjecture
In This Way but Nicely. Pattern Avoidance. Follow-Up.
Containing a Pattern Many Times
Containing a Pattern a Given Number of Times
Mean and Insensitive. Random Permutations.
The Probabilistic Viewpoint
Variance and Standard Deviation
An Application: Longest Increasing Subsequences
Permutations versus Everything Else. Algebraic Combinatorics of Permutations.
The Robinson–Schensted–Knuth Correspondence
Posets of Permutations
Simplicial Complexes of Permutations
Get Them All. Algorithms and Permutations.
Stack Sorting Permutations
Variations of Stack Sorting
How Did We Get Here? Permutations as Genome Rearrangements.
Block Transpositions Revisited
Solutions to Odd-Numbered Exercises
List of Frequently Used Notation