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Combinatorics of Set Partitions

Publisher: 
Chapman & Hall/CRC
Number of Pages: 
587
Price: 
99.95
ISBN: 
9781439863336
Date Received: 
Wednesday, October 24, 2012
Reviewable: 
Yes
Include In BLL Rating: 
No
Reviewer Email Address: 
Toufik Mansour
Series: 
Discrete Mathematics and Its Applications
Publication Date: 
2013
Format: 
Hardcover
Category: 
Monograph

Introduction
Historical Overview and Earliest Results
Timeline of Research for Set Partitions
A More Detailed Book

Basic Tools of the Book
Sequences
Solving Recurrence Relations

Generating Functions
Lagrange Inversion Formula
The Principle of Inclusion and Exclusion
Generating Trees

Preliminary Results on Set Partitions
Dobiński’s Formula
Different Representations

Subword Statistics on Set Partitions
Subword Patterns of Size Two: Rises, Levels and Descents
Peaks and Valleys
Subword Patterns: -Rises, -Levels, and -Descents
Families of Subword Patterns
Patterns of Size Three

Nonsubword Statistics on Set Partitions
Statistics and Block Representation
Statistics and Canonical and Rook Representations
Records and Weak Records
Number of Positions between Adjacent Occurrences of a Letter
The Internal Statistic
Statistics and Generalized Patterns
Major Index
Number of Crossings, Nestings and Alignments

Avoidance of Patterns in Set Partitions
History and Connections
Avoidance of Subsequence Patterns
Generalized Patterns
Partially Ordered Patterns

Multi Restrictions on Set Partitions
Avoiding a Pattern of Size Three and Another Pattern
Pattern Avoidance in Noncrossing Set Partitions
General Equivalences
Two Patterns of Size Four
Left Motzkin Numbers
Sequence A054391
Catalan and Generalized Catalan Numbers
Pell Numbers
Regular Set Partitions
Distance Restrictions
Singletons
Block-Connected

Asymptotics and Random Set Partition
Tools from Probability Theory
Tools from Complex Analysis
Z-Statistics
Set Partitions as Geometric Words
Asymptotics for Set Partitions

Gray Codes, Loopless Algorithms and Set Partitions
Gray Code and Loopless Algorithms
Gray Codes for Pn
Loopless Algorithm for Generating Pn

Set Partitions and Normal Ordering
Preliminaries
Linear Representation and N((aa)n)
Wick’s Theorem and q-Normal Ordering
p-Normal Ordering
Noncrossing Normal Ordering

Appendices

Bibliography

Index

Publish Book: 
Modify Date: 
Wednesday, October 24, 2012

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