Combinatorics of Compositions and Words
Seiten
2009
Chapman & Hall/CRC (Verlag)
978-1-4200-7267-9 (ISBN)
Chapman & Hall/CRC (Verlag)
978-1-4200-7267-9 (ISBN)
Provides an introduction to the methods used in the combinatorics of pattern avoidance and pattern enumeration in compositions and words. This book describes the strengths and weaknesses of a wide variety of solution techniques and approaches, presents an overview of the field, and illustrates fresh methods and definitions with worked examples.
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.
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.
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.
Introduction. Basic Tools of the Trade. Compositions. Statistics on Compositions. Avoidance of Non-Subword Patterns in Compositions. Words. Automata and Generating Trees. Asymptotics for Compositions. Appendices. References.
| Erscheint lt. Verlag | 22.7.2009 |
|---|---|
| Reihe/Serie | Discrete Mathematics and Its Applications |
| Zusatzinfo | 38 Tables, black and white; 50 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 1850 g |
| Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
| Mathematik / Informatik ► Mathematik | |
| ISBN-10 | 1-4200-7267-6 / 1420072676 |
| ISBN-13 | 978-1-4200-7267-9 / 9781420072679 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
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