Introduction To Enumerative And Analytic Combinatorics

Miklós Bóna

Taylor & Francis Group

WINNER of a CHOICE Outstanding Academic Title Award for 2006! As linear orders, as elements of the symmetric group, modeled by matrices, modeled by graphs…permutations are omnipresent in modern combinatorics. They are omnipresent but also multifaceted, and while several excellent books explore particular aspects of the subject, no one book has covered them all. Even the classic results are scattered in various resources. Combinatorics of Permutations offers the first comprehensive, up to date treatment of both enumerative and extremal combinatorics and looks at permutation as linear orders and as elements of the symmetric group. The author devotes two full chapters to the young but active area of pattern avoidance. He explores the quest for the Stanley-Wilf conjecture and includes the recent and spectacular Marcus-Tardos proof of this problem. He examines random permutations and Standard Young Tableaux and provides an overview of the very rich algebraic combinatorics of permutations. The final chapter takes an in-depth look at combinatorial sorting algorithms. The author's style is relaxed, entertaining, and clearly reflects his enthusiasm for the "serious fun" the subject holds. Filled with applications from a variety of fields and exercises that draw upon recent research results, this book serves equally well as a graduate-level text and a reference for combinatorics researchers.

Combinatorics of Permutations (Discrete Mathematics and Its Applications)

Computers & Technology

Computer Science

Chapman and Hall/CRC

A Walk Through Combinatorics

This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity.As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

Science & Math

Mathematics

World Scientific Pub Co Inc

The first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are.\nNew to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises - more than a hundred in total - which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.

Walk Through Combinatorics (5ed)

Programming

Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Second Edition)

World Scientific

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