Combinatorics of Compositions and Words

1. Auflage 2009
ISBN: 978-1-4200-7267-9
Verlag: Taylor & Francis Ltd

Buch, Englisch, 504 Seiten, Format (B × H): 164 mm x 242 mm, Gewicht: 895 g

Reihe: Discrete Mathematics and Its Applications

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.

Autoren/Hrsg.

Heubach, Silvia

Mansour, Toufik (University of Haifa, Israel)

Mansour, Toufik

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Informatik

Inhaltsverzeichnis

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.

Über Autor(innen)

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.