Kozlov, D.
Combinatorial Algebraic Topology
Springer-Verlag 2008.
390 pp.(H)
ISBN 3-540-71961-X
13,100円
Contents
1. Overture/ Part I. Concepts of Algebraic Topology: 2. Cell Complexes/ 3. Homology Groups/ 4. Concepts of Category Theory as Functors/ 5. Exact Sequences/ 6. Homotopy/ 7. Cofibrations/ 8. Principal ?-Bundles and Stiefel-Whitney Characteristic Classes/ Part II. Methods of Combinatorial Algebraic Topology: 9. Combinatorial Complexes Melange 10. Acyclic Categories/ 11. Discrete Morse Theory/ 12. Lexicographic Shellability/ 13. Evasiveness and Closure Operators/ 14. Colimits and Quotients/ 15. Homotopy Colimits/ 16. Spectral Sequences/ Part III. Complexes of Graph Homomorphisms: 17. Chromatic Numbers and the Kneser Conjecture/ 18. Structural Theory of Morphism Complexes/ 19. Characteristic Classes and Chromatic Numbers 20. Applications of Spectral Sequences to Hom Complexes/ References/ Index/
* Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. *
Korte, B. & Vygen, J.
Combinatorial Optimization 4th ed.
Springer-Verlag 2008.
627 pp.(H)
ISBN 3-540-71843-5
9,100円
Contents
1.Introduction/ 2.Graphs/ 3.Linear Programming/ 4.Linear Programming Algorithms/ 5.Integer Programming/ 6.Spanning Trees and Arborescence/ 7.Shortest Paths/ 8.Network Flows/ 9.Minimum Cost Flows/ 10.Maximum Matchings/ 11.Weighted Matching/ 12.b-Machings and T-Joins/ 13.Matroids/ 14.Generalizations of Matroids/ 15.NP^Completeness/ 16.Approximation Algorithms/ 17.The Knapsack Problem/ 18.Bin-Packing/ 19.Multicommodity Flows and Edge-Disjoint Paths/ 20.Network Design Problems/ 21.The Traveling Salesman Problem/ 22.Facility Location/ Notation Index/ Author Index/ Subject Index/ *
Gross, J. L.
Combinatorial Methods with Computer Applications
Chapman & Hall/ CRC 2007.11
644 pp. (H)
ISBN 1-58488-743-5
13,400円
Contents
1.Introduction to Combinatorics/ 2.Sequences/ 3.Solving Recurrences/ 4.Evaluating Sums/ 5.Subsets and Binomials/ 6.Partitions and Permutations/ 7.Integer Operations/ 8.Graph Fundamentaals/ 9.Graph Theory Topics/ 10.Graph Enumeration/ 11.Designs/ 12.Appendix/ 13.Bibliography/ 14.Solutions and Hints/ 15.Indices/ index/
* Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course. *
Jungnickel, D.
Graphs, Networks and Algorithms 3rd ed.
Springer-Verlag 2008.
650 pp. (H)
ISBN 3-540-72779-5
11,700円
Contents
1. Basic Graph Theory/ 2. Algorithms and Complexity/ 3. Shortest Paths/ 4. Spanning Trees/ 5. The Greedy Algorithm/ 6. Flows/ 7. Combinatorial Applications/ 8. Connectivity and Depth First Search/ 9. Colorings/ 10. Circulations/ 11. The Network Simplex Algorithm/ 12. Synthesis of Networks/ 13. Matchings/ 14. Weighted matchings/ 15. A Hard Problem: The TSP/ A. Some NP-Complete Problems/ B. Solutions: B.1. Solutions for Chapter 1/ B.2. Solutions for Chapter 2/ B.3. Solutions for Chapter 3/ B.4. Solutions for Chapter 4/ B.5. Solutions for Chapter 5/ B.6. Solutions for Chapter 6/ B.7. Solutions for Chapter 7/ B.8. Solutions for Chapter 8/ B.9. Solutions for Chapter 9/ B.10. Solutions for Chapter 10/ B.11. Solutions for Chapter 11/ B.12. Solutions for Chapter 12/ B.13. Solutions for Chapter 13/ B.14. Solutions for Chapter 14/ Contents XIX/ B.15. Solutions for Chapter 15/ C. List of Symbols: C.1. General Symbols/ C.2. Special Symbols/ References/ Index/
* The third edition of this standard textbook contains additional material: two new application sections (on graphical codes and their decoding) and about two dozen further exercises (with solutions, as throughout the text). Moreover, recent developments have been discussed and referenced, in particular for the travelling salesman problem. The presentation has been improved in many places (for instance, in the chapters on shortest paths and on colorings), and a number of proofs have been reorganized, making them more precise or more transparent. *
Mishra, S.K. et al.
V-Invex Functions and Vector Optimization
Springer-Verlag 2008.1
164 pp. (H)
ISBN 0-387-75445-8
12,000円
Contents
1.Preface/ 2.General Introduction/ 3.V-Invexity In Nonlinear Multiobjective Programming/ 4.Multiobjective Fractional Programming/ 5.Multiobjective Nonsmooth Programming/ 6.Composite Multiobjective Nonsmooth Programming/ 7.Continuous-Time Programming/ References/ Index/ *
Jeyakumar, V. & Luc, D.T.
Nonsmooth Vector Functions and Continuous Optimization
Springer-Verlag 2008.1
270 pp. (H)
ISBN 0-387-73716-2
10,800円
Contents
1.Preface/ 2.Pseudo-Jacobian Matrices/ 3.Calculus Rules for Pseudo-Jacobians/ 4.Openness of Continuous Vector Functions/ 4.Nonsmooth Mathematical Programming Problems/ 5.Monotone Operators and Nonsmooth Variational Inequalities/ 6.Bibliographical Notes/ References/ Notations/ Index/ *
928-11 登録日 08.02.11
