Combinatorics (English Edition, 4th Edition)

Author: Brualdi
Publisher:
Publication Date: 2005-03-01
Features: This book is an excellent textbook that systematically elaborates on the fundamentals, theories, methods, and examples of combinatorics. For nearly 30 years since its publication, it has been revised multiple times and has been adopted by many prestigious universities abroad, such as MIT, Columbia University, UIUC, and the University of Wisconsin, significantly impacting combinatorics education both domestically and internationally. It is also one of the main reference books for related disciplines. The book focuses on the concepts and ideas of combinatorics, including the pigeonhole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, the inclusion-exclusion principle, generating functions, and recurrence relations, as well as combinatorial structures (matchings, experimental designs, graphs). It concisely and clearly expresses the author's comprehensive and profound understanding of the field, introducing numerous historical examples derived from mathematical games and entertainment. The perfect treatment of Polya counting and Burnside's theorem, among others, makes it accessible even to students unfamiliar with group theory. In addition to including the content of the third edition, this edition has been updated with the addition of M?bius inversion (as an extension of the inclusion-exclusion principle), lattice paths, and Schr?der numbers. Furthermore, each chapter contains a large number of exercises, and reference answers and hints are provided at the end of the book. This book is an excellent textbook that systematically elaborates on the fundamentals, theories, methods, and examples of combinatorics. For nearly 30 years since its publication, it has been revised multiple times and has been adopted by many prestigious universities abroad, such as MIT, Columbia University, UIUC, and the University of Wisconsin, significantly impacting combinatorics education both domestically and internationally. It is also one of the main reference books for related disciplines. The book focuses on the concepts and ideas of combinatorics, including the pigeonhole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, the inclusion-exclusion principle, generating functions, and recurrence relations, as well as combinatorial structures (matchings, experimental designs, graphs). It concisely and clearly expresses the author's comprehensive and profound understanding of the field, introducing numerous historical examples derived from mathematical games and entertainment. The perfect treatment of Polya counting and Burnside's theorem, among others, makes it accessible even to students unfamiliar with group theory. In addition to including the content of the third edition, this edition has been updated with the addition of M?bius inversion (as an extension of the inclusion-exclusion principle), lattice paths, and Schr?der numbers. Furthermore, each chapter contains a large number of exercises, and reference answers and hints are provided at the end of the book.