Volume: 219; 2021; 398 pp; Softcover
MSC: Primary 14; 52; 90;
Print ISBN: 978-1-4704-6741-8
Product Code: GSM/219.S
List Price: $85.00
AMS Member Price: $68.00
MAA Member Price: $76.50
Electronic ISBN: 978-1-4704-6740-1
Product Code: GSM/219.E
List Price: $85.00
AMS Member Price: $68.00
MAA Member Price: $76.50
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Supplemental Materials
Essentials of Tropical Combinatorics
Share this pageMichael Joswig
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using \(\texttt{polymake}\).
Readership
Graduate students and researchers interested in combinatorial, polyhedral, and optimization aspects (as opposed to algebraic geometry aspects) of tropical geometry.
Table of Contents
Table of Contents
Essentials of Tropical Combinatorics
- Cover Cover11
- Title page iii4
- Preface xiii14
- Notation xvii18
- Chapter 1. Tropical Hypersurfaces 122
- Chapter 2. Fields of Power Series and Tropicalization 2748
- Chapter 3. Graph Algorithms and Polyhedra 5980
- Chapter 4. Products of Tropical Polynomials and the Cayley Trick 97118
- Chapter 5. Tropical Convexity 127148
- Chapter 6. Combinatorics of Tropical Polytopes 159180
- Chapter 7. Tropical Half-Spaces 191212
- Chapter 8. Tropical Linear Programming 215236
- Chapter 9. Feasibility and Mean Payoffs 253274
- Chapter 10. Matroids and Tropical Linear Spaces 281302
- Appendix A. Geometric Combinatorics 333354
- Appendix B. Computational Complexity 341362
- Appendix C. Using \polymake 347368
- Appendix D. Hints to Selected Problems 367388
- Bibliography 373394
- Index 393414
- Back Cover Back Cover1421