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© LIBERO v6.4.1sp220816
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Catalogue Tag Display
Catalogue Tag Display
MARC 21
Combinatorial Theory
Tag
Description
020
$a9781461566663
082
$a510
099
$aOnline resource: Springer
100
$aAigner, Martin$d1942-
245
$aCombinatorial Theory$h[EBook]$cby Martin Aigner
260
$aNew York, NY$bSpringer New York$c1979
300
$aVIII, 484 p.$bonline resource.
336
$atext
338
$aonline resource
440
$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v234
505
$a
Preliminaries -- 1. Sets -- 2. Graphs -- 3. Posets -- 4. Miscellaneous Notation -- I. Mappings -- 1. Classes of Mappings -- 2. Fundamental Orders -- 3. Permutations -- 4. Patterns -- Notes -- II. Lattices -- 1. Distributive Lattices -- 2. Modular and Semimodular Lattices -- 3. Geometric Lattices -- 4. The Fundamental Examples -- Notes -- III. Counting Functions -- 1. The Elementary Counting Coefficients -- 2. Recursion and Inversion -- 3. Binomial Sequences -- 4. Order Functions -- Notes -- IV. Incidence Functions -- 1. The Incidence Algebra -- 2. Möbius Inversion -- 3. The Möbius Function -- 4. Valuations -- Notes -- V. Generating Functions -- 1. Ordered Structures -- 2. Unordered Structures -- 3. G-patterns -- 4. G,H-patterns -- Notes -- VI. Matroids: Introduction -- 1. Fundamental Concepts -- 2. Fundamental Examples -- 3. Construction of Matroids -- 4. Duality and Connectivity -- Notes -- VII. Matroids: Further Theory -- 1. Linear Matroids -- 2. Binary Matroids -- 3. Graphic Matroids -- 4. Transversal Matroids -- Notes -- VIII. Combinatorial Order Theory -- 1. Maximum-Minimum Theorems -- 2. Transversal Theorems -- 3. Sperner Theorems -- 4. Ramsey Theorems -- Notes -- List of Symbols.
520
$a
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).
538
$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710
$aSpringerLink (Online service)
830
$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$v234
856
$u
http://dx.doi.org/10.1007/978-1-4615-6666-3
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