Combinatorics of Set Partitions

Toufik Mansour

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English

Chapman & Hall/CRC
14 October 2024

Discrete mathematics; Combinatorics & graph theory; Automatic control engineering

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.

By: Toufik Mansour
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 1.140kg
ISBN: 9781032919126
ISBN 10: 1032919124
Pages: 616
Publication Date: 14 October 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Reviews for Combinatorics of Set Partitions

"""Containing 375 references, this book works best as an encyclopedia for researchers working in this topic. But it can also be effectively used by students who are interested in the combinatorics of set partitions and want to get a hand on researching them. … a very useful reference for researchers of the enumerative side of set partitions."" —Acta Sci. Math. (Szeged), 80, 2014 ""… a comprehensive account of the history and current research in the combinatorics of pattern enumeration and pattern avoidance in set partitions. … While it is aimed primarily at advanced undergraduate and graduate students in discrete mathematics with a focus on set partitions, its extensive bibliography, with 375 entries, and the variety of constructions and approaches used in the text make it a valuable reference for researchers in this field."" —Ricardo Mamede, Zentralblatt MATH 1261 ""… a comprehensive account of recent and current research on the pattern-related aspects of set partitions."" —David Callan, Mathematical Reviews, April 2013"