Combinatorics of Compositions and Words

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CRC Press, Jul 20, 2009 - Mathematics - 504 pages
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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 MapleTM and Mathematica®, as well as C++ to perform computations.

 

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Contents

Introduction
1
Basic Tools of the Trade
23
Compositions
61
Statistics on Compositions
89
Avoidance of Nonsubword Patterns in Compositions
131
Words
193
Automata and Generating Trees
245
Asymptotics for Compositions
311
Chebychev Polynomials of the Second Kind
371
Probability Theory
375
Complex Analysis Review
381
Using Mathematica and Maple
385
C++ and Maple Programs
399
Notation
445
References
453
Index
467

Useful Identities and Generating Functions
359
Linear Algebra and Algebra Review
363

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About the author (2009)

Silvia Heubach is a Professor and the Chair of the Department of Mathematics at the California State University, Los Angeles, where she received the Outstanding Professor Award in 1999/2000.

Toufik Mansour is an Associate Professor at the University of Haifa. The author or co-author of more than 60 papers, Professor Mansour’s general research interest is in discrete mathematics and its applications, with an emphasis on pattern avoidance problems.

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