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Synopsis
It is now generally recognized that the field of combinatorics has, over the past years, evolved into a fully-fledged branch of discrete mathematics whose potential with respect to computers and the natural sciences is only beginning to be realized. Still, two points seem to bother most authors: The apparent difficulty in defining the scope of combinatorics and the fact that combinatorics seems to consist of a vast variety of more or less unrelated methods and results. As to the scope of the field, there appears to be a growing consensus that combinatorics should be divided into three large parts: (a) Enumeration, including generating functions, inversion, and calculus of finite differences; (b) Order Theory, including finite posets and lattices, matroids, and existence results such as Hall's and Ramsey's; (c) Configurations, including designs, permutation groups, and coding theory. The present book covers most aspects of parts (a) and (b), but none of (c). The reasons for excluding (c) were twofold. First, there exist several older books on the subject, such as Ryser [1] (which I still think is the most seductive introduction to combinatorics), Hall [2], and more recent ones such as Cameron-Van Lint [1] on groups and designs, and Blake-Mullin [1] on coding theory, whereas no compre hensive book exists on (a) and (b).
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Review
From the reviews: "This book presents a very good introduction to combinatorics. It covers most aspects of enumeration and order theory,... It is divided into three parts. The first part presents the basic material on mappings and posets... The second part deals with enumeration ... Finally the third part treats of the order-theoretic aspects ... In the text examples are given and at the end of each chapter valuable notes, also very good selected exercises. They constitute an organic part of the book. This book can warmly be recommended first of all to students interested in combinatorics. A two semester course can also be based on it."
Publicationes Mathematicae Debrecen
About the Author
Biography of Martin Aigner
Martin Aigner received his Ph.D. in Mathematics in 1965 from the University of Vienna. He then spent five years in the United States, the last two at the University of North Carolina at Chapel Hill where he was introduced to the combinatorial world (which he has never left since) by G. C. Rota and the late R. C. Bose. After extensive travels he returned to Europe and spent three years at the University of Tübingen with a senior fellowship of the German Science Foundation. Since 1974 he has been a Professor of Mathematics at the Free University of Berlin.
Martin Aigner has published in various fields of combinatorics and graph theory and is the author of several monographs on discrete mathematics, graph theory and the theory of search.
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- PublisherSpringer
- Publication date2012
- ISBN 10 1461566681
- ISBN 13 9781461566687
- BindingPaperback
- LanguageEnglish
- Number of pages492
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