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Triangulations: Structures for Algorithms and Applications
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 presentsExpand
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A counterexample to the Hirsch conjecture
  • F. Santos
  • Mathematics, Computer Science
  • ArXiv
  • 14 June 2010
The Hirsch Conjecture (1957) stated that the graph of a d-dimensional polytope with n facets cannot have (combinatorial) diameter greater than n d. Expand
  • 192
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Higher Lawrence configurations
We introduce a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. Expand
  • 78
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On the rank of a tropical matrix
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 oneExpand
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The Polytope of All Triangulations of a Point Configuration
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 ofExpand
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Expansive Motions and the Polytope of Pointed Pseudo-Triangulations
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 theExpand
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The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings
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 aExpand
  • 88
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Pseudo-Triangulations - a Survey
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 dataExpand
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An effective version of Pólya's theorem on positive definite forms
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
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The polytope of non-crossing graphs on a planar point set
For any finite set A of n points in general position in R2, 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, where a marked graph is a geometric graph together with a subset of its pointed vertices. Expand
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