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5 papers · 2 filters
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…
Expansive Motions and the Polytope of Pointed Pseudo-Triangulations
Guenter Rote, Francisco Santos, Ileana Streinu
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…
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…
Non-connected toric Hilbert schemes
Francisco Santos
We construct small (50 and 26 points, respectively) point sets in dimension 5 whose graphs of triangulations are not connected. These examples improve our construction in J. Amer.…