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(TM) 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, 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(TM) 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.
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.
Inhaltsangabe
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.
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.
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