Books by Toufik Mansour

This book provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. It discusses the Stirling numbers, closely related generalizations, and their role as normal ordering coefficients in the Weyl algebra. In addition to the combinatorial aspects, the book presents the relation to operational calculus and describes the physical motivation for ordering words in the Weyl algebra arising from quantum theory, along with some applications.

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.