Walk Through Combinatorics : An Introduction to Enumeration and Graph Theory

Bona, Miklos

ISBN 10: 9814460001 / ISBN 13: 9789814460002

Editore: Wspc, 2011

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Dati bibliografici

• Titolo: Walk Through Combinatorics : An Introduction to Enumeration and Graph Theory
• Editore: Wspc
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 9814460001
• ISBN 13: 9789814460002
• Rilegatura: Brossura
• Edizione: terza edizione
• Condizione: New

Descrizione articolo

Riassunto

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.

Recensione

The chapters on block designs and counting unlabeled structures have been added to the third edition, and there are also one hundred new problems in the other eighteen chapters. When I next teach a combinatorics course, this will be the text I use. --Mathematical Reviews

This is still one of the best introductions to combinatorics. --Mathematical Association of America