Multi-triangulations as complexes of starpolygons (2009)
Vincent Pilaud, Francisco Santos
Abstract. Maximal (k+1)-crossing-free graphs on a planar point set in convex position, that is, k-triangulations, have received attention in recent literature, with motivation coming from several...
An update on the Hirsch conjecture: Fifty-two years later (2009)
Santos, Francisco, Kim, Edward D.
The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n -...
Maximizing Maximal Angles for Plane Straight-Line Graphs ⋆ (2009)
Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, Clemens Huemer, Attila Pór, Francisco Santos, ...
Abstract. Let G =(S, E) be a plane straight-line graph on a finite point set S ⊂ R 2 in general position. The incident angles of a point p ∈ S in G are the angles between any two edges of G that...
David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, Walter Whiteley
Abstract. We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing...
Contemporary Mathematics Pseudo-Triangulations — a Survey (2008)
Günter Rote, Francisco Santos, Ileana Streinu
Abstract. A pseudo-triangle is a simple polygon with exactly three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations...
Maximizing Maximal Angles for Plane Straight Line Graphs (2008)
Oswin Aichholzer, Thomas Hackl, Francisco Santos
Let G =(S, E) be a plane straight line graph on a finite point set S ⊂ R 2 in general position. For a point p ∈ S let the maximum incident angle of p in G be the maximum angle between any two...
( de Gruyter 2003 Alexander duality in subdivisions of Lawrence polytopes (2008)
Francisco Santos, Bernd Sturmfels
(Communicated by G. Ziegler) Abstract. The class of simplicial complexes representing triangulations and subdivisions of Lawrence polytopes is closed under Alexander duality. This gives a new...
THE GENERALIZED BAUES PROBLEM FOR CYCLIC POLYTOPES II (2008)
Cyclic Polytopes Ii, Christos A. Athanasiadis, Francisco Santos, The Generalized
WHICH ARE INDUCED BY THE MAP has the homotopON tS Ope of A SPHERE. WE EXTEND earlier work of the last two authors on subdivisio of cyclic polBEtopes to YCive an affirmative answer to the problem for...
Contemporary Mathematics Pseudo-Triangulations — a Survey (2008)
Günter Rote, Francisco Santos, Ileana Streinu
Abstract. A pseudo-triangle is a simple polygon with exactly three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations...
Maximizing Maximal Angles for Plane Straight Line Graphs (2008)
Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, Clemens Huemer, Francisco Santos
Let G =(S, E) be a plane straight line graph on a finite point set S ⊂ R 2 in general position. For a point p ∈ S let the maximum incident angle of p in G be the maximum angle between any two...
Contemporary Mathematics Pseudo-Triangulations — a Survey (2008)
Günter Rote, Francisco Santos, Ileana Streinu
Abstract. A pseudo-triangle is a simple polygon with exactly three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations...
Lattice points in Minkowski sums (2007)
Haase, Christian, Nill, Benjamin, Paffenholz, Andreas, Santos, Francisco
Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal...
Extremal properties for dissections of convex 3-polytopes (2007)
Francisco Santos, Fumihiko Takeuchi
Abstract. A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the...
On The Topology Of The Baues Poset Of Polyhedral Subdivisions (2007)
Christos Athanasiadis And, Christos A. Athanasiadis, Francisco Santos
. Given an affine projection : P ! Q of convex polytopes, let !(P; ) be the refinement poset of proper polyhedral subdivisions of Q which are induced by , in the sense of Billera and Sturmfels. Let !...
The number of triangulations of the cyclic polytope C(n,n-4) (2007)
Miguel Azaola, Francisco Santos
We show that the exact number of triangulations of the cyclic polytope C(n; n \Gamma 4) is (n + 4)2 n\Gamma4 2 \Gamma n if n is even and i 3n+11 2 p 2 j 2 n\Gamma4 2 \Gamma n if n is odd. These...
Extremal Properties for Dissections of Convex Polytopes (2007)
Francisco Santos, Fumihiko Takeuchi
. A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional...
Monotone Paths On Zonotopes And Oriented Matroids (2007)
Christos A. Athanasiadis, FRANCISCO SANTOS
. Monotone paths on zonotopes and the natural generalization to maximal chains in the poset of topes of an oriented matroid or arrangement of pseudo-hyperplanes are studied with respect to a kind of...
On the number of facets of three-dimensional Dirichlet stereohedra I: Groups with reflexions (2007)
Daciana Bochi Francisco, Francisco Santos
Let G be a crystallographic group in IR n . A Dirichlet stereohedron for G is any region in the Voronoi diagram of any orbit of G. We prove that Dirichlet stereohedra for three-dimensional...
We study a constructive method to find an algebraic curve in the real projective plane with a (possibly singular) topological type given in advance. Our method works if the topological model T to be...
Serkan Hosten, Francisco Santos, Bernd Sturmfels, Communicated Gunter, M. Ziegler
Abstract. We study the convex hull PA of the 0-1 incidence vectors of all triangulations of a point configuration A. This was called the universal polytope in [4]. The affine span of PA is described...
Francisco Santos, Ileana Streinu
The line numbers in the margins should encourage you to quickly report any errors that you spot to the authors. Remarks of any other kind are equally welcome. (If you don't like those numbers,...
Günter Rote, Francisco Santos, Ileana Streinu
We introduce the polytope of pointed pseudo-triangulations, defined as the polytope of expansive motions of a planar point set subject to certain constraints on the increase of their distances. Its...
Asymptotically Efficient Triangulations of the d-Cube (2007)
Triangulating the regular d-cube I^d = [0, 1]^d in a "simple" way has many applications, like solving differential equations by finite element methods or calculating fixed points. See, for...
Graphs of Transportation Polytopes (2007)
De Loera, Jesús A., Kim, Edward D., Onn, Shmuel, Santos, Francisco
This paper discusses properties of the graphs of 2-way and 3-way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results include a quadratic...
On the Number of Facets of Three-Dimensional Dirichlet Stereohedra IV: Quarter Cubic Groups (2007)
Sabariego, Pilar, Santos, Francisco
In this paper we finish the intensive study of three-dimensional Dirichlet stereohedra started by the second author and D. Bochis, who showed that they cannot have more than 80 facets, except perhaps...
Multi-triangulations as complexes of star polygons (2007)
Pilaud, Vincent, Santos, Francisco
Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several...
Maximizing Maximal Angles for Plane Straight-Line Graphs (2007)
Aichholzer, Oswin, Hackl, Thomas, Hoffmann, Michael, Huemer, Clemens, Por, Attila, Santos, Francisco, ...
Let $G=(S, E)$ be a plane straight-line graph on a finite point set $S\subset\R^2$ in general position. The \emph{incident angles} of a point $p \in S$ in $G$ are the angles between any two edges of...
Triple-loop networks with arbitrarily many minimum distance diagrams (2007)
Sabariego, Pilar, Santos, Francisco
Minimum distance diagrams are a way to encode the diameter and routing information of multi-loop networks. For the widely studied case of double-loop networks, it is known that each network has at...
On the number of pseudo-triangulations of certain point sets (2007)
Oswin Aichholzer, David Orden, Francisco Santos, Bettina Speckmann
We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double...
On the number of pseudo-triangulations of certain point sets (2007)
Oswin Aichholzer, David Orden, Francisco Santos, Bettina Speckmann
We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it in two prominent families of point sets, namely the so-called double circle and double...
Pseudo-Triangulations - a Survey (2006)
Rote, Guenter, Santos, Francisco, Streinu, Ileana
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...
On the Number of Facets of Three-Dimensional Dirichlet Stereohedra III: Full Cubic Groups (2006)
Sabariego, Pilar, Santos, Francisco
We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic groups can have. The problem for non-cubic groups was studied in previous...
Geometric bistellar flips. The setting, the context and a construction (2006)
We give a self-contained introduction to the theory of secondary polytopes and geometric bistellar flips in triangulations of polytopes and point sets, as well as a review of some of the known...
On the Number of Pseudo-Triangulations of Certain Point Sets (2006)
Aichholzer, Oswin, Orden, David, Santos, Francisco, Speckmann, Bettina
We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double...
The Gromov Norm of the Product of Two Surfaces (2004)
Bowen, Lewis, De Loera, Jesus A., Develin, Mike, Santos, Francisco
We make an estimation of the value of the Gromov norm of the Cartesian product of two surfaces. Our method uses a connection between these norms and the minimal size of triangulations of the products...
Non-crossing frameworks with non-crossing reciprocals (2004)
David Orden, G Ünter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, Walter Whiteley
Abstract. We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2004)
Ruth Haas, David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than π). In this paper we prove that the opposite...
The Cayley trick and triangulations of products of simplices (2003)
We use the Cayley Trick to study polyhedral subdivisions of the product of two simplices. For arbitrary (fixed) $l$, we show that the numbers of regular and non-regular triangulations of...
Non-crossing frameworks with non-crossing reciprocals (2003)
Orden, David, Rote, Guenter, Santos, Francisco, Servatios, Brigitte, Servatius, Herman, Whiteley, Walter
We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing frameworks...
Combinatorial pseudo-Triangulations (2003)
Orden, David, Santos, Francisco, Servatius, Brigitte, Servatius, Herman
We prove that a planar graph is generically rigid in the plane if and only if it can be embedded as a pseudo-triangulation. This generalizes the main result of math.CO/0307347 which treats the...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2003)
Haas, Ruth, Orden, David, Rote, Guenter, Santos, Francisco, Servatius, Brigitte, Servatius, Herman, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than 180 degrees. In this paper we prove that the opposite...
The polytope of non-crossing graphs on a planar point set (2003)
Orden, David, Santos, Francisco
For any finite set $\A$ of $n$ points in $\R^2$, we define a $(3n-3)$-dimensional simple polyhedron whose face poset is isomorphic to the poset of ``non-crossing marked graphs'' with vertex set $\A$,...
Expansive motions and the polytope of pointed pseudo-triangulations (2003)
Günter 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 constraints on the...
Expansive motions and the polytope of pointed pseudo-triangulations (2003)
Gunter 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 constraints on the...
Expansive motions and the polytope of pointed pseudo-triangulations (2003)
Francisco Santos, Ileana Streinu
We introduce the polytope of pointed pseudo-triangulations, dened as the polytope of expansive motions of a planar point set subject to certain constraints on the increase of their distances. Its...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2003)
Ruth Haas, David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Hermann Servatius, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (incident to an angle larger than #). In this paper we prove that the opposite statement is...
Higher Lawrence configurations (2002)
Santos, Francisco, Sturmfels, Bernd
Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove finiteness results...
Expansive Motions and the Polytope of Pointed Pseudo-Triangulations (2002)
Rote, Guenter, Santos, Francisco, Streinu, Ileana
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...
On the number of facets of three-dimensional Dirichlet stereohedra II: Non-cubic Groups (2002)
Bochis, Daciana, Santos, Francisco
We prove that Dirichlet stereohedra for non-cubic crystallographic groups in dimension 3 cannot have more than 80 facets. The bound depends on the particular crystallographic group considered and is...
Asymptotically efficient triangulations of the d-cube (2002)
Orden, David, Santos, Francisco
Let $P$ and $Q$ be polytopes, the first of "low" dimension and the second of "high" dimension. We show how to triangulate the product $P \times Q$ efficiently (i.e., with few simplices) starting with...
Non-connected toric Hilbert schemes (2002)
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. Math. Soc., 13:3...
A better upper bound on the number of triangulations of a planar point set (2002)
Santos, Francisco, Seidel, Raimund
We show that a point set of cardinality $n$ in the plane cannot be the vertex set of more than $59^n O(n^{-6})$ straight-edge triangulations of its convex hull. This improves the previous upper bound...
Alexander duality in subdivisions of Lawrence polytopes (2002)
Santos, Francisco, Sturmfels, Bernd
The class of simplicial complexes representing triangulations and subdivisions of Lawrence polytopes is closed under Alexander duality. This gives a new geometric model for oriented matroid duality.
Counting triangulations and pseudo-triangulations of wheels (2001)
Dana Randall, Gunter Rote, Francisco Santos, Jack Snoeyink
Motivated by several open questions on triangulations and pseudotriangulations, we give closed form expressions for the number of triangulations and the number of minimum pseudo-triangulations of n...
Counting triangulations and pseudo-triangulations of wheels (2001)
Dana Randall, Gunter Rote, Francisco Santos, Jack Snoeyink
Motivated by several open questions on triangulations and pseudotriangulations, we give closed form expressions for the number of triangulations and the number of minimum pseudo-triangulations of n...
Counting Triangulations and Pseudo-Triangulations of Wheels (2001)
Dana Randall College, Dana Randall, Francisco Santos, Günter Rote, Jack Snoeyink
Motivated by several open questions on triangulations and pseudotriangulations, we give closed form expressions for the number of triangulations and the number of minimum pseudo-triangulations of n...
Expansive Motions and the Polytope of Pointed Pseudo-Triangulations (2001)
Günter 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 constraints on the...
c ○ 2001 Universitat de Barcelona On the refinements of a polyhedral subdivision (2001)
Let π:P →Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by π (or π-induced) and the...
Extremal properties for dissections of convex 3-polytopes (2000)
De Loera, Jesús A., Santos, Francisco, Takeuchi, Fumihiko
A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional...
A point set whose space of triangulations is disconnected (2000)
In this paper we explicitly construct a triangulation of a 6-dimensional point configuration of 324 points which admits no geometric bistellar operations (or flips, for short). This triangulation is...
Realizable but not strongly euclidean oriented matroids, preprint (2000)
The extension space conjecture of oriented matroid theory claims that the space of all (non-zero, non-trivial, single-element) extensions of a realizable oriented matroid of rank r is homotopy...
A Point Set Whose Space of Triangulations is Disconnected (2000)
this paper we construct explicitly a triangulation of a 6-dimensional point configuration of 324 points which admits no geometric bistellar operations (or flips,
On the Refinements of a Polyhedral Subdivision (2000)
Let : P ! Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by (or -induced) and the fiber...
On The Topology Of The Baues Poset Of Polyhedral Subdivisions (2000)
Christos A. Athanasiadis, Francisco Santos
. Given an affine projection : P ! Q of convex polytopes, let !(P; ) be the refinement poset of proper polyhedral subdivisions of Q which are induced by , in the sense of Billera and Sturmfels. Let !...
Realizable But Not Strongly Euclidean Oriented Matroids (2000)
The extension space conjecture of oriented matroid theory claims that the space of all (non-zero, non-trivial, single-element) extensions of a realizable oriented matroid of rank r is homotopy...
The generalized Baues problem for cyclic polytopes II (1999)
Christos A. Athanasiadis, Jörg Rambau, Francisco Santos
Given an affine surjection of polytopes : P! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map has the homotopy type of a...
A Point Set Whose Space of Triangulations is Disconnected (1999)
By the "space of triangulations" of a finite point configuration A we mean either of the following two objects: the partially order set (poset) of all polyhedral subdivisions of A (the...
The Generalized Baues Problem for Cyclic Polytopes II (1999)
Preprint Sc Januar, Christos A. Athanasiadis, Christos A. Athanasiadis, J Org Rambau, J Org Rambau, Francisco Santos, ...
. Given an affine surjection of polytopes ß : P ! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map ß has the homotopy...
The Graph of Triangulations of a Point Configuration With D+4 Vertices is 3-Connected. (1999)
Miguel Azaola, Francisco Santos
We study the graph of bistellar flips between triangulations of a vector configuration A with d + 4 elements in rank d + 1 (i.e. with corank 3), as a step in the Baues problem. We prove that the...
The Cayley Trick, Lifting Subdivisions And The Bohne-Dress Theorem On Zonotopal Tilings (1999)
Birkett Huber, Jörg Rambau, J Org Rambau, Francisco Santos
. 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 Minkowski...
The generalized Baues problem for cyclic polytopes I (1999)
An important special case of the Generalized Baues Problem asks whether the order complex of all proper polyhedral subdivisions of a given point configuration, partially ordered by refinement, is...
The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings (1999)
Preprint Sc, J Org, Rambau Francisco Santos, Birkett Huber, Birkett Huber, J Org Rambau, ...
. 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 Minkowski...
The number of geometric bistellar neighbors of a triangulation (1999)
Francisco Santos, Jorge Urrutia
The theory of secondary and fiber polytopes implies that regular (also called convex or coherent) triangulations of configurations with n points in R
On bisectors for convex distance functions in 3-space (1999)
Christian Icking, Rolf Klein, Ngoc-minh Lê, Lihong Ma, Francisco Santos
We investigate the structure of the bisector of point sites under arbitrary convex distance functions in three dimensions. Our results show that it is advantageous for analyzing bisectors to consider...
On Bisectors for Convex Distance Functions in 3-Space (1999)
Christian Icking, Rolf Klein, Ngoc-minh Lê, Lihong Ma, Francisco Santos
We investigate the structure of the bisector of point sites under arbitrary convex distance functions in three dimensions. Our results show that it is advantageous for analyzing bisectors to consider...
The Cayley trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings (1999)
Birkett Huber, Birkett Huber, Jorg Rambau, Francisco Santos, Francisco Santos
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...
The Generalized Baues Problem For Cyclic Polytopes (1998)
. The Generalized Baues Problem asks whether for a given point configuration the order complex of all its proper polyhedral subdivisions, partially ordered by refinement, is homotopy equivalent to a...
The Generalized Baues Problem For Cyclic Polytopes II (1998)
Christos A. Athanasiadis, Jörg Rambau, J Org Rambau, Francisco Santos
. Given an affine surjection of polytopes ß : P ! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map ß has the homotopy...
Triangulations With Very Few Geometric Bistellar Neighbors (1998)
We are interested in a notion of elementary change between triangulations of a point configuration, the so-called bistellar flips, introduced by Gel'fand, Kapranov and Zelevinski. We construct...
Fiber Polytopes For The Projections Between Cyclic Polytopes (1997)
Christos Athanasiadis Jes, Christos A. Athanasiadis, Victor Reiner, Francisco Santos
. The cyclic polytope C(n; d) is the convex hull of any n points on the moment curve f(t; t 2 ; : : : ; t d ) : t 2 Rg in R d . For d 0 ? d, we consider the fiber polytope (in the sense of Billera...
Triangulations Of Oriented Matroids (1997)
We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-- Munson and by Anderson and which specializes to the usual...
Fiber Polytopes For The Projections Between Cyclic Polytopes (1997)
Christos Athanasiadis, Victor Reiner, Francisco Santos
. The cyclic polytope C(n; d) is the convex hull of any n points on the moment curve f(t; t 2 ; : : : ; t d ) : t 2 Rg in R d . For d 0 ? d, we consider the fiber polytope (in the sense of Billera...
Fiber Polytopes For The Projections Between Cyclic Polytopes (1997)
Christos A. Athanasiadis, Victor Reiner, Francisco Santos
. The cyclic polytope C(n; d) is the convex hull of any n points on the moment curve f(t; t 2 ; : : : ; t d ) : t 2 Rg in R d . For d 0 ? d, we consider the fiber polytope (in the sense of Billera...
The Polytope of All Triangulations of a Point Configuration (1996)
Serkan Hosten, Francisco Santos, Bernd Sturmfels
We study the convex hull PA of the 0-1 incidence vectors of all triangulations of a point configuration A. This was called the universal polytope in [4]. The affine span of PA is described in terms...
Inscribing a Symmetric Body in an Ellipse. (1996)
We prove that any bounded, centrally symmetric object K in the plane can be inscribed in an ellipse E touching its boundary @K at at least four points. An application to Minkowski geometry is given....
The Number Of Geometric Bistellar Neighbors Of A Triangulation (1996)
Jes'us A. Loera, Francisco Santos, Jorge Urrutia
The theory of secondary and fiber polytopes implies that regular (also called convex or coherent) triangulations of configurations with n points in R d have at least n \Gamma d \Gamma 1 geometric...
An effective version of Pólya's theorem on positive definite forms (1995)
Francisco Santos, Facultad De Ciencias
Given a real homogeneous polynomial F , strictly positive in the non-negative orthant, P'olya's theorem says that for a sufficiently large exponent p the coefficients of F (x1 ; . . . ; xn...
On Delaunay Oriented Matroids. (1995)
: The fact that for any finite set S of points in the Euclidean plane E 2 one can define an oriented matroid in terms of how spheres partition it is well-known and easy to proof via the lifting...
On Delaunay Oriented Matroids For Convex Distance Functions. (1995)
For any finite point set S in E d , an oriented matroid DOM(S) can be defined in terms of how S is partitioned by Euclidean hyperspheres. This oriented matroid is related to the Delaunay...
Impacto das Marcas na Produção: uma análise a partir dos dados do INPI
Francisco Santos, Adriano Baesa, Gustavo Costa, Fernando Freitas
The aim of this paper is to measure the impact of trademarks over firms´ economic performance using microdata from Instituto Nacional de Propriedade Industrial (INPI), the brazilian intellectual...
Does Social Capital Affect Entrepreneurial Intentions?
Francisco Liñán, Francisco Santos
Entrepreneurship, Entrepreneurial intention, Social capital, M00, Z13,
Graphs of Transportation Polytopes
Jesús A. De, Loera Edward, D. Kim, Shmuel Onn, Francisco Santos
This paper discusses properties of the graphs of 2-way and 3-way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results include a quadratic...