Book Project: Essentials of Tropical Combinatorics

by Michael Joswig

This web page is dedicated to a forthcoming book on combinatorial aspects of tropical geometry.

Here is a near complete current draft. Each page shows a git-hash, followed by a time stamp like, e.g., [bbb39bb, 2020-04-30 18:16:05 +0200] at the bottom. All comments are most welcome, especially those including time-stamps and line numbers. Please re-check for regular updates: new versions are available at least once a week.

Below is the table of contents; the final chapter on matroids is still missing in the current draft.

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 final version will feature short appendices on ordinary polytopes, computational complexity and polymake. The current versions of the Appendices A (polytopes) and C (polymake) are now part of this draft.

• polymake code for Appendix D available on github