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AuthorAigner, Martin. author
TitleCombinatorial Theory [electronic resource] / by Martin Aigner
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997
Connect tohttp://dx.doi.org/10.1007/978-3-642-59101-3
Descript X, 483 p. online resource

SUMMARY

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)


CONTENT

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. Mรถbius Inversion -- 3. The Mรถbius 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


Mathematics Algebra Ordered algebraic structures Convex geometry Discrete geometry Combinatorics Mathematics Combinatorics Convex and Discrete Geometry Order Lattices Ordered Algebraic Structures



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