Combinatorics of Set Partitions

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.

Introduction. Basic Tools of the Book. Generating Functions. Preliminary Results on Set Partitions. Subword Statistics on Set Partitions. Nonsubword Statistics on Set Partitions. Avoidance of Patterns in Set Partitions. Multi Restrictions on Set Partitions. Asymptotics and Random Set Partition. Gray Codes, Loopless Algorithms and Set Partitions. Set Partitions and Normal Ordering. Appendices. Bibliography. Index.

Toufik Mansour is a professor in the Department of Mathematics at the University of Haifa. Dr. Mansour has authored/co-authored more than 200 papers and is a reviewer for many journals, including Advances in Applied Mathematics, Discrete Mathematics, Discrete Applied Mathematics, European Journal of Combinatorics, and the Journal of Combinatorial Theory Series A. His research focuses on pattern avoidance in permutations, colored permutations, set partitions, words, and compositions.