Combinatorics of Set Partitions

Toufik Mansour

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July 27, 2012 by Chapman and Hall/CRC
Reference - 516 Pages - 38 B/W Illustrations
ISBN 9781439863336 - CAT# K12931
Series: Discrete Mathematics and Its Applications

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Features

  • Provides a self-contained, accessible introduction to historical and current research on enumeration of and pattern avoidance in set partitions
  • Presents several links between set partitions and areas of mathematics and physics
  • Describes a variety of tools and approaches useful in other topics of enumerative combinatorics
  • Includes open questions for further research or projects as well as an extensive bibliography
  • Contains end-of-chapter exercises, with hints and solutions in an appendix
  • Offers C++ programs and their outputs on the author’s web page

Summary

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.