Essentials of tropical combinatorics

著者

    • Joswig, Michael

書誌事項

Essentials of tropical combinatorics

Michael Joswig

(Graduate studies in mathematics, 219)

American Mathematical Society, c2021

  • : hardback

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注記

Includes bibliographical references (p. 373-391) and index

内容説明・目次

内容説明

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 $\texttt{polymake}$.

目次

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

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