1st Edition
Combinatorics of Compositions and Words
Introduction
Historical Overview—Compositions
Historical Overview—Words
A More Detailed Look
Basic Tools of the Trade
Sequences
Solving Recurrence Relations
Generating Functions
Compositions
Definitions and Basic Results (One Variable)
Restricted Compositions
Compositions with Restricted Parts
Connection between Compositions and Tilings
Colored Compositions and Other Variations
Research Directions and Open Problems
Statistics on Compositions
History and Connections
Subword Patterns of Length 2: Rises, Levels, and Drops
Longer Subword Patterns
Research Directions and Open Problems
Avoidance of Non-Subword Patterns in Compositions
History and Connections
Avoidance of Subsequence Patterns
Generalized Patterns and Compositions
Partially Ordered Patterns in Compositions
Research Directions and Open Problems
Words
History and Connections
Definitions and Basic Results
Subword Patterns
Subsequence Patterns—Classification
Subsequence Patterns—Generating Functions
Generalized Patterns of Type (2,1)
Avoidance of Partially Ordered Patterns
Research Directions and Open Problems
Automata and Generating Trees
History and Connections
Tools from Graph Theory
Automata
Generating Trees
The ECO Method
Research Directions and Open Problems
Asymptotics for Compositions
History
Tools from Probability Theory
Tools from Complex Analysis
Asymptotics for Compositions
Asymptotics for Carlitz Compositions
A Word on the Asymptotics for Words
Research Directions and Open Problems
Appendix A: Useful Identities and Generating Functions
Appendix B: Linear Algebra and Algebra Review
Appendix C: Chebychev Polynomials of the Second Kind
Appendix D: Probability Theory
Appendix E: Complex Analysis Review
Appendix F: Using Mathematica and Maple
Appendix G: C++ and Maple Programs
Appendix H: Notation
References
Exercises appear at the end of each chapter.
Biography
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.
… contains a lot of hidden gems, which need to be explored. It is an advantage that the authors provide fragments of Maple and Mathematica code which would help such explorations. … The book is written in an accessible style … it is quite easy to use for the non-specialist in the area, given a basic computer science and/or mathematical background. It will be a useful reference for the researcher, as well as a very good textbook for a graduate-level course in the area. I recommend the book heartily to both specialists and beginning researchers in the area.
—IACR Book Reviews, June 2011
