Combinatorics of Set Partitions [Hardcover]

Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitionspresents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Designed for students and researchers in discrete mathematics, the book is a one-stop reference on the results and research activities of set partitions from 1500 A.D. to today.

Each chapter gives historical perspectives and contrasts different approaches, including generating functions, kernel method, block decomposition method, generating tree, and Wilf equivalences. Methods and definitions are illustrated with worked examples and Maple code. End-of-chapter problems often draw on data from published papers and the authors extensive research in this field. The text also explores research directions that extend the results discussed. C++ programs and output tables are listed in the appendices and available for download on the authors web page.

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
DobiDskis 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

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