Combinatorics of Permutations
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A CHOICE "Outstanding Academic Title," the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, third edition continues to clearly show the usefulness of this subject for both students and researchers.
The research in combinatorics of permutations has advanced rapidly since this book was published in a first edition. Now the third edition offers not only updated results, it remains the leading textbook for a course on the topic.
Coverage is mostly enumerative, but there are algebraic, analytic, and topological parts as well, and applications.
Since the publication of the second edition, there is tremendous progress in pattern avoidance (Chapters 4 and 5). There is also significant progress in the analytic combinatorics of permutations, which will be incorporated.
•A completely new technique from extremal combinatorics disproved a long-standing conjecture, and this is presented in Chapter 4.
•The area of universal permutations has undergone a lot of very recent progress, and that has been noticed outside the academic community as well. This also influenced the revision of Chapter 5.
•New results in stack sorting are added to Chapter 8.
•Chapter 9 applications to biology has been revised.
The author’s other works include Introduction to Enumerative and Analytic Combinatorics, second edition (CHOICE "Outstanding Academic Title") and Handbook of Enumerative Combinatorics, published by CRC Press. The author also serves as Series Editor for CRC’s Discrete Mathematics and Its Applications.
Table of Contents
Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
Introduction: No Way around It.
1.In One Line and Close: Permutations as Linear Orders
2.In One Line and Anywhere: Permutations as Linear Orders- Inversions
3.In Many Circles: Permutations as Products of Cycles
4.In Any Way but This: Pattern Avoidance—the Basics
5.In This Way, but Nicely: Pattern Avoidance-Follow Up
6.Mean and Insensitive: Random Permutations
7.Permutations and the Rest: Algebraic Combinatorics of Permutations
8.Get Them All: Algorithms and Permutations
9.How Did We Get Here? Permutations as Genome Rearrangements
Do Not Look Just Yet: Solutions to Odd-Numbered Exercises
List of Frequently Used Notation
Miklós Bóna received his Ph.D in mathematics from the Massachusetts Institute of Technology in 1997. Since 1999, he has taught at the University of Florida, where, in 2010, he was inducted into the Academy of Distinguished Teaching Scholars. Professor Bóna has mentored numerous graduate and undergraduate students. He is the author of four books and more than 65 research articles, mostly focusing on enumerative and analytic combinatorics. His book, Combinatorics of Permutations, won a 2006 Outstanding Title Award from Choice, the journal of the American Library Association. He is also an editor-in-chief for the Electronic Journal of Combinatorics, and for two book series at CRC Press.