Combinatorics of Permutations 2nd Edition by Miklos Bona ISBN 1439850518 9781439850510
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ISBN 10: 1439850518
ISBN 13: 9781439850510
Author: Miklos Bona
A Unified Account of Permutations in Modern CombinatoricsA 2006 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, Second Edition continues to clearly show the usefuln
Combinatorics of Permutations 2nd Table of contents:
Chapter 1: Introduction to Permutations
1.1 Basic Definitions and Notation
1.2 Factorials and Counting Principles
1.3 Permutations vs Combinations
1.4 Basic Properties of Permutations
Chapter 2: Permutation Groups
2.1 Group Actions on Sets
2.2 Symmetric Groups
2.3 Cycles and Cycle Notation
2.4 Transpositions and Their Properties
2.5 Decomposition of Permutations into Cycles
Chapter 3: Counting Permutations with Restrictions
3.1 Permutations with Repetitions
3.2 Derangements
3.3 Permutations with Forbidden Positions
3.4 Involutions and Other Special Classes
Chapter 4: Patterns and Pattern Avoidance
4.1 Introduction to Pattern Containment
4.2 Pattern Avoidance in Permutations
4.3 Wilf-Equivalence
4.4 Enumerative Results and Generating Functions
Chapter 5: Permutation Statistics
5.1 Inversions
5.2 Descents and Ascents
5.3 Major Index and Other Statistics
5.4 Eulerian Numbers and Related Distributions
Chapter 6: Generating Functions and Recurrences
6.1 Ordinary and Exponential Generating Functions
6.2 Recurrence Relations for Permutations
6.3 Applications to Counting Problems
Chapter 7: Advanced Topics in Permutations
7.1 Coxeter Groups and Reflection Groups
7.2 Young Tableaux and the Robinson-Schensted-Knuth Correspondence
7.3 Permutations in Algebraic Combinatorics
7.4 Connections to Representation Theory
Chapter 8: Applications and Algorithms
8.1 Algorithms for Generating Permutations
8.2 Applications in Sorting and Searching
8.3 Permutations in Cryptography and Coding Theory
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Tags: Miklos Bona, Miklos Bona