# Combinatorial Theory

• Martin Aigner
Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 234)

1. Front Matter
Pages i-viii
2. Martin Aigner
Pages 1-4
3. Martin Aigner
Pages 5-29
4. Martin Aigner
Pages 30-72
5. Martin Aigner
Pages 73-136
6. Martin Aigner
Pages 137-195
7. Martin Aigner
Pages 196-254
8. Martin Aigner
Pages 255-321
9. Martin Aigner
Pages 322-390
10. Martin Aigner
Pages 391-451
11. Back Matter
Pages 453-483

### Introduction

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).

### Keywords

Combinatorics Counting Finite Lattice Permutation algebra calculus discrete mathematics duality function mapping mathematics order theory recursion theorem

#### Authors and affiliations

• Martin Aigner
• 1
1. 1.II. Institut für MathematikFreie Universität BerlinBerlin 33Federal Republic of Germany

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4615-6666-3
• Copyright Information Springer-Verlag New York 1979
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4615-6668-7
• Online ISBN 978-1-4615-6666-3
• Series Print ISSN 0072-7830
• Buy this book on publisher's site
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