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Combinatorial Theory : Classics in Mathematics - Martin Aigner

Combinatorial Theory

Classics in Mathematics

Paperback Published: February 1997
ISBN: 9783540617877
Number Of Pages: 483

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Preliminaries: Sets: Graphs; Posets; Miscellaneous Notation. Mappings: Classes of Mappings; Fundamental Orders; Permutations; Patterns. Lattices: Distributive Lattices; Modular and Semimodular Lattices; Geometric Lattices; The Fundamental Examples. Countng Functions: The Elementary Counting Coefficients; Recursion and Inversion; Binomial Sequences; Order Functions. Incidence Functions: The Incidence Algebra; Möbius Inversion; The Möbius Function; Valuations. Generating Functions:Ordered Structures; Unordered Structures; G-patterns; G, H-patterns. Matroids- Introduction: Fundamental Concepts; Fundamental Examples; Construction of Matroids; Duality and Connectivity. Matroids - Further Theory: Linear Matroids; Bineary matroids; Graphic Matroids; Transversal Matroids. Combinatorial Order Theory: Maximum-Minimum Theorems; Transversal Theorems; Sperner Theorems; Ramsey Theorems. Bibliography. List of Symbols. Subject Index

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

Preliminaries :Sets : Graphs
Miscellaneous Notation.
Classes of Mappings
Fundamental Orders
Lattices: Distributive Lattices
Modular and Semimodular Lattices
Geometric Lattices
The Fundamental Examples
Countng Functions: The Elementary Counting Coefficients
Recursion and Inversion
Binomial Sequences
Order Functions
Incidence Functions: The Incidence Algebra
The M
Generating Functions:Ordered Structures
Unordered Structures
G, H-patterns
Matroids- Introduction
Fundamental Concepts
Fundamental Examples
Construction of Matroids
Duality and Connectivity
Matroids - Further Theory: Linear Matroids
Bineary matroids
Graphic Matroids
Transversal Matroids
Combinatorial Order Theory: Maximum-Minimum Theorems
Transversal Theorems
Sperner Theorems
Ramsey Theorems
List of Symbols
Subject Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540617877
ISBN-10: 3540617876
Series: Classics in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 483
Published: February 1997
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.62 x 15.8  x 2.64
Weight (kg): 0.66

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