Combinatorics of Compositions and Words

Silvia Heubach, Toufik Mansour

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July 20, 2009 by Chapman and Hall/CRC
Reference - 504 Pages - 50 B/W Illustrations
ISBN 9781420072679 - CAT# C7267
Series: Discrete Mathematics and Its Applications

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Features

  • Presents a historical overview of the field
  • Describes the strengths and weaknesses of a wide variety of solution techniques and approaches
  • Includes tables that list the classification of patterns according to Wilf-equivalence for subsequence patterns and generalized patterns in words and compositions
  • Illustrates new methods and definitions with worked examples and Maple and Mathematica code where applicable
  • Offers C++ programs to compute the number of compositions and words with certain characteristics
  • Contains known and new results, end-of-chapter exercises, and directions for future research
  • Provides an extensive set of references on research in compositions, k-ary words, and pattern avoidance problems

Solutions manual available for qualifying instructors

Summary

A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel Research Directions

Focusing on a very active area of research in the last decade, Combinatorics of Compositions and Words provides an introduction to the methods used in the combinatorics of pattern avoidance and pattern enumeration in compositions and words. It also presents various tools and approaches that are applicable to other areas of enumerative combinatorics.

After a historical perspective on research in the area, the text introduces techniques to solve recurrence relations, including iteration and generating functions. It then focuses on enumeration of basic statistics for compositions. The text goes on to present results on pattern avoidance for subword, subsequence, and generalized patterns in compositions and then applies these results to words. The authors also cover automata, the ECO method, generating trees, and asymptotic results via random compositions and complex analysis.

Highlighting both established and new results, this book explores numerous tools for enumerating patterns in compositions and words. It includes a comprehensive bibliography and incorporates the use of the computer algebra systems Maple™ and Mathematica®, as well as C++ to perform computations.