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- Publications
- Influence
Triangulations: Structures for Algorithms and Applications
- J. D. Loera, Jörg Rambau, F. Santos
- Mathematics
- 16 August 2010
Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book studies the subdivisions and triangulations of polyhedral regions and point sets and presents… Expand
A counterexample to the Hirsch conjecture
- F. Santos
- Mathematics, Computer Science
- ArXiv
- 14 June 2010
TLDR
Higher Lawrence configurations
- F. Santos, B. Sturmfels
- Mathematics, Computer Science
- J. Comb. Theory, Ser. A
- 24 September 2002
TLDR
On the rank of a tropical matrix
- M. Develin, F. Santos, B. Sturmfels
- Mathematics
- 5 December 2003
An apparatus (10) for use in securing a specimen (S) in a folding specimen holder (58) having an arm blade (12). A spring clip (26) releasably secures the grid (58) to the arm blade (12) so that one… Expand
The Polytope of All Triangulations of a Point Configuration
- J. D. Loera, S. Hosten, F. Santos, Bernd Sturmfels
- Mathematics
- 1996
We study the convex hull P A of the 0-1 incidence vectors of all triangulations of a point con guration A. This was called the universal polytope in [4]. The a ne span of P A is described in terms of… Expand
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Expansive Motions and the Polytope of Pointed Pseudo-Triangulations
- G. Rote, F. Santos, I. Streinu
- Mathematics
- 4 June 2002
We introduce the polytope of pointed pseudo-triangulations of a point set in the plane, defined as the polytope of infinitesimal expansive motions of the points subject to certain constraints on the… Expand
The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings
- B. Huber, Jörg Rambau, F. Santos
- Mathematics
- 30 June 2000
Abstract.In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a… Expand
Pseudo-Triangulations - a Survey
- G. Rote, F. Santos, I. Streinu
- Mathematics
- 21 December 2006
A pseudo-triangle is a simple polygon with three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations appear as data… Expand
An effective version of Pólya's theorem on positive definite forms
- J. D. Loera, F. Santos
- Mathematics
- 13 May 1996
Abstract Given a real homogeneous polynomial F , strictly positive in the non-negative orthant, Polya's theorem says that for a sufficiently large exponent p the coefficients of F ( x 1 ,…, x n ) · (… Expand
The polytope of non-crossing graphs on a planar point set
TLDR