Combinatorics of Set Partitions

Focusing on a very active area of mathematical research in the last decade, this book presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Each chapter gives historical perspectives, contrasts different approaches, and illustrates methods and definitions with worked examples and Maple™ code. The text also explores research directions and includes end-of-chapter problems that often draw on real-world data. C++ programs and output tables are listed in the appendices and available for download online.

Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents 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 author’s 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 author’s web page.