Essentials of Tropical Combinatorics
(Sprache: Englisch)
This introduction to a current hot topic explains, at the graduate student level, how tropical geometry can be accessed via geometric combinatorics. The book's central concept is Develin and Sturmfels version of tropical linear algebra, tropical convexity .
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This introduction to a current hot topic explains, at the graduate student level, how tropical geometry can be accessed via geometric combinatorics. The book's central concept is Develin and Sturmfels version of tropical linear algebra, tropical convexity .
Klappentext zu „Essentials of Tropical Combinatorics “
The goal of this book is to explain, at the graduate student level, how tropical geometry can be accessed via geometric combinatorics. This way the book offers a viable path to a topic of very active research. At the same time the reader learns how a number of seemingly unrelated combinatorial results fall into place, once viewed through the tropical lens . No attempt is made to cover the entire field of tropical geometry, which has been evolving too rapidly anyway to be covered by a book so small. The book's central concept is the tropical convexity introduced by Develin and Sturmfels, which is a version of tropical linear algebra . This is used in the book as a general language to study classical subjects in combinatorial optimization including shortest paths, the assignment problem, the even dicycle problem, flow-type problems, and others.
This book focuses on the polyhedral and combinatorial aspects of tropical geometry while requiring less prerequisites in algebraic geometry and commutative algebra, thus making the book more accessible to a wider audience. The main requirement beyond general mathematical maturity is a basic knowledge in polytope theory.
Inhaltsverzeichnis zu „Essentials of Tropical Combinatorics “
Preface.- Contents.- Introduction.- 1 Tropical Arithmetic and Polynomials.- 2 Puiseux Series and Tropicalization.- 3 Graph Algorithms and the Tropical Determinant.- 4 Tropical Polytopes.- 5 Products of Simplices.- 6 Tropical Halfspaces.- 7 Polytropes.- 8 Resolutions of Monomial Ideals.- 9 Tropical Linear Spaces.- 10 Matroid Subdivisions of Hypersimplices.- 11 Buildings.- 12Using polymake.- Appendix A Ordinary Convex Polytopes.- Appendix B Matroids and Oriented Matroids.- Appendix C Gröbner Bases.- Bibliography.- Index
Autoren-Porträt von Michael Joswig
Michael Joswig is currently a professor of mathematics at Technische Universität Darmstadt. His mathematical interests include geometric combinatorics, discrete differential geometry, combinatorial topology, discrete optimization, mathematical software, and related areas.
Bibliographische Angaben
- Autor: Michael Joswig
- 2014, 180 Seiten, 50 Schwarz-Weiß-Abbildungen, Maße: 23,5 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 1441983651
- ISBN-13: 9781441983657
Sprache:
Englisch
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