Combinatorics of Compositions and Words

Highlighting both established and new results, this book provides an introduction to the methods used in the combinatorics of pattern avoidance and pattern enumeration in compositions and words. It describes the strengths and weaknesses of a wide variety of solution techniques and approaches, presents a historical overview of the field, and illustrates new methods and definitions with worked examples. The text also incorporates the use of Maple™, Mathematica^®, and C++ to perform computations. It includes a comprehensive bibliography, exercises at the end of each chapter, and directions for future research. A solutions manual is available for qualifying instructors.

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.