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.

This book is a carefully written exposition of Coxeter groups, an area of mathematics which appears in algebra, geometry, and combinatorics. In this book, the combinatorics of Coxeter groups has mainly to do with reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this book will be presenting the combinatorial aspects of Coxeter groups. The authors have included an exposition of Coxeter groups along with a rich variety of exercises, ranging from easy to very difficult, giving the book the unique character of serving as both a textbook and a monograph.

There are 650 articles with the word permutation in the title whose primary classification is combinatorics, but, until now, there have been no books addressing the topic. The very first book to be published on the subject, Combinatorics of Permutations contains a comprehensive, up to date treatment of the subject. Covering both enumerative and external combinatorics, this book can be used as either a graduate text or as a reference for professional mathematicians. The book includes many applications from computer science, probabilistic methods, and pattern avoidance, and the numerous exercises show readers a fairly comprehensive list of recent results from the field.

This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001.The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover topics such as: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability, complexity and constructive mathematics; discrete mathematics, combinatorial computing and category theory; logic, nonmonotonic logic and hybrid systems; molecular computing.

The areas represented in this collection range from set theory and geometry through graph theory, group theory and combinatorial probability, to randomized algorithms and statistical physics. Erd?s himself was able to give a survey of recent progress made on his favorite problems. Consequently this volume, comprised of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.

Including many algorithms described in simple terms, this book stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter.

Mathematical Association of America
November 18, 2009

Description

Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, P???????3lya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.

The Mathematical Association of America
January 14, 1999

Description

This book is unique in that it combines features of a traditional text with those of a problem book. The material is presented through a series of problems with connecting text. The problems are structured in order to introduce concepts in a logical order, and in a thought-provoking way.