Introduction To Enumerative Combinatorics
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Introduction to Enumerative Combinatorics
Author: Miklós Bóna
language: en
Publisher: McGraw-Hill Science/Engineering/Math
Release Date: 2007
Written by one of the leading authors and researchers in the field, this comprehensive modern text offers a strong focus on enumeration, a vitally important area in introductory combinatorics crucial for further study in the field. Miklós Bóna's text fills the gap between introductory textbooks in discrete mathematics and advanced graduate textbooks in enumerative combinatorics, and is one of the very first intermediate-level books to focus on enumerative combinatorics. The text can be used for an advanced undergraduate course by thoroughly covering the chapters in Part I on basic enumeration and by selecting a few special topics, or for an introductory graduate course by concentrating on the main areas of enumeration discussed in Part II. The special topics of Part III make the book suitable for a reading course. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Introduction to Enumerative and Analytic Combinatorics, Second Edition
Divided into three parts, this book fills in the gap between introductory texts in discrete mathematics and advanced graduate textbooks in enumerative combinatorics. Part I deals with basic counting principles, compositions and partitions, and generating functions. Part II focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Finally, Part III covers supplemental topics, including error-correcting codes, properties of sequences, and magic squares.
Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Third Edition)
Author: Miklos Bona
language: en
Publisher: World Scientific Publishing Company
Release Date: 2011-05-09
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.The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected].