66 citations · 568 across the 67 of their papers we have counts for
6 papers · 1 filter
Tropical Computations in polymake
Simon Hampe, Michael Joswig
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our…
Algorithms for Tight Spans and Tropical Linear Spaces
Simon Hampe, Michael Joswig, Benjamin Schröter
We describe a new method for computing tropical linear spaces and more general duals of polyhedral subdivisions. It is based on Ganter's algorithm (1984) for finite closure systems…
A tropical isoperimetric inequality
Jules Depersin, Stéphane Gaubert, Michael Joswig
We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is element…
Matroids from hypersimplex splits
Michael Joswig, Benjamin Schröter
A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases. As their key feature these split matroids can be studied via tec…
The Cayley Trick for Tropical Hypersurfaces With a View Toward Ricardian Economics
Michael Joswig
The purpose of this survey is to summarize known results about tropical hypersurfaces and the Cayley Trick from polyhedral geometry. This allows for a systematic study of arrangeme…
The polymake XML file format
Ewgenij Gawrilow, Simon Hampe, Michael Joswig
We describe an XML file format for storing data from computations in algebra and geometry. We also present a formal specification based on a RELAX-NG schema.