Author | Aigner, Martin. author |
---|---|
Title | Combinatorial Theory [electronic resource] / by Martin Aigner |
Imprint | New York, NY : Springer New York, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-6666-3 |
Descript | VIII, 484 p. online resource |
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. 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