69 citations · 92 across the 3 of their papers we have counts for
7 papers
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…
The Cayley trick and triangulations of products of simplices
Francisco Santos
We use the Cayley Trick to study polyhedral subdivisions of the product of two simplices. For arbitrary (fixed) , we show that the numbers of regular and non-regular triangulati…
The polytope of non-crossing graphs on a planar point set
David Orden, Francisco Santos
For any finite set $\A$ of points in , we define a -dimensional simple polyhedron whose face poset is isomorphic to the poset of ``non-crossing marked graphs'' wi…
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…
A better upper bound on the number of triangulations of a planar point set
Francisco Santos, Raimund Seidel
We show that a point set of cardinality in the plane cannot be the vertex set of more than straight-edge triangulations of its convex hull. This improves the p…
Asymptotically efficient triangulations of the d-cube
David Orden, Francisco Santos
Let and be polytopes, the first of "low" dimension and the second of "high" dimension. We show how to triangulate the product efficiently (i.e., with few simpl…