102 citations · 200 across the 13 of their papers we have counts for
8 papers · 1 filter
Matroid polytopes, nested sets and Bergman fans
Eva Maria Feichtner, Bernd Sturmfels
The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid po…
Tropical Mathematics
David Speyer, Bernd Sturmfels
These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture…
On the rank of a tropical matrix
M. Develin, F. Santos, B. Sturmfels
This is a foundational paper in tropical linear algebra, which is linear algebra over the min-plus semiring. We introduce and compare three natural definitions of the rank of a mat…
Short Rational Functions for Toric Algebra and Applications
Jesus De Loera, David Haws, Raymond Hemmecke +3
We encode the binomials belonging to the toric ideal associated with an integral matrix using a short sum of rational functions as introduced by Barvinok \ci…
Higher Lawrence configurations
Francisco Santos, Bernd Sturmfels
Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove…
Supernormal Vector Configurations
Serkan Hosten, Diane Maclagan, Bernd Sturmfels
A configuration of lattice vectors is supernormal if it contains a Hilbert basis for every cone spanned by a subset. We study such configurations from various perspectives, includi…