
Essentials of Tropical Combinatorics
Michael Joswig(Author)
American Mathematical Society (Publisher)
Published on 1. November 2021
Book
Hardback
406 pages
978-1-4704-6653-4 (ISBN)
Article exhausted; check different version
Description
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 Universitat 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 $\texttt{polymake}$.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
916 gr
ISBN-13
978-1-4704-6653-4 (9781470466534)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
Tropical hypersurfaces
Fields of power series and tropicalization
Graph algorithms and polyhedra
Products of tropical polynomials and the Cayley trick
Tropical convexity
Combinatorics of tropical polytopes
Tropical half-spaces
Tropical linear programming
Feasibility and mean payoffs
Matroids and tropical linear spaces
Geometric combinatorics
Computational complexity
Using $\texttt{polymake}$
Hints to selected problems
Bibliography
Index
Fields of power series and tropicalization
Graph algorithms and polyhedra
Products of tropical polynomials and the Cayley trick
Tropical convexity
Combinatorics of tropical polytopes
Tropical half-spaces
Tropical linear programming
Feasibility and mean payoffs
Matroids and tropical linear spaces
Geometric combinatorics
Computational complexity
Using $\texttt{polymake}$
Hints to selected problems
Bibliography
Index