Combinatorial Theory /
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...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1979
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| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ;
234 |
| Subjects: | |
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Table of Contents:
- 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