102 citations · 200 across the 13 of their papers we have counts for
8 papers · 1 filter
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…
Algebraic Recipes for Integer Programming
Bernd Sturmfels
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear ob…
Tropical Convexity
Mike Develin, Bernd Sturmfels
The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regula…
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…
First steps in tropical geometry
Jürgen Richter-Gebert, Bernd Sturmfels, Thorsten Theobald
Tropical algebraic geometry is the geometry of the tropical semiring . Its objects are polyhedral cell complexes which behave like complex algebraic varieties.…
The Tropical Grassmannian
David Speyer, Bernd Sturmfels
In tropical algebraic geometry, the solution sets of polynomial equations are piecewise-linear. We introduce the tropical variety of a polynomial ideal, and we identify it with a p…