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Catalogue Information
Field name
Details
Dewey Class
511.6
Title
Combinatorial Theory ([EBook]) / by Martin Aigner.
Author
Aigner, Martin , 1942-
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : Springer Berlin Heidelberg , 1997
Physical Details
X, 483 p. : online resource.
Series
Classics in mathematics
1431-0821
ISBN
9783642591013
Summary Note
Reihentext + Combinatorial Theory 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).:
Contents note
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 Function -- 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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-642-59101-3
Links to Related Works
Subject References:
Algebra
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Combinatorics
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Convex and Discrete Geometry
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Convex geometry
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Discrete geometry
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Mathematics
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Order, Lattices, Ordered Algebraic Structures
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Ordered algebraic structures
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Authors:
Aigner, Martin 1942-
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Corporate Authors:
SpringerLink (Online service)
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Series:
Classics in mathematics
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Classification:
511.6
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