Book Project: Essentials of Tropical Combinatorics

by Michael Joswig

This web page is dedicated to a forthcoming book on combinatorial aspects of tropical geometry. It will appear in the series Graduate Studies in Mathematics, published by the AMS.

Here is a near complete draft. Each page shows a git-hash, followed by a time stamp like, e.g., [f7530cb, 2020-11-15 18:38:04 +0100] at the bottom. All comments are most welcome, especially those including time-stamps and line numbers.

Below is the table of contents.

1. Tropical Hypersurfaces
2. Fields of Puiseux Series
3. Graph Algorithms and Polyhedra
4. Products of Tropical Polynomials and the Cayley Trick
5. Tropical Convexity
6. Combinatorics of Tropical Polytopes
7. Tropical Halfspaces
8. Tropical Linear Programming
9. Feasibility and Mean Payoffs
10. Matroids and Tropical Linear Spaces

Additionally the book features short appendices on ordinary polytopes (A), computational complexity (B), polymake (C) and hints to solutions of selected problems (D).

• polymake code for Appendix C available on github