Nonregular Triangulations, View Graphs of Triangulations, and Linear Programming Duality
نویسنده
چکیده
For a triangulation and a point, we de ne a directed graph representing the order of the maximal dimensional simplices in the triangulation viewed from the point. We prove that triangulations having a cycle the reverse of which is not a cycle in this graph viewed from some point are forming a (proper) subclass of nonregular triangulations. We use linear programming duality to investigate further properties of nonregular triangulations in connection with this graph.
منابع مشابه
Combinatorics of Triangulations Title: Associate Professor of Information Science
Several combinatorial aspects of triangulations and their generalizations are studied in this thesis. A triangulation of a point con guration and a d-dimensional polyhedron whose vertices are among the points is a decomposition of the polyhedron using d-simplices with vertices among the points. The two main elds triangulations appear are combinatorial geometry in mathematics and computational g...
متن کاملTitle: Associate Professor of Information Science
Several combinatorial aspects of triangulations and their generalizations are studied in this thesis. A triangulation of a point con guration and a d-dimensional polyhedron whose vertices are among the points is a decomposition of the polyhedron using d-simplices with vertices among the points. The two main elds triangulations appear are combinatorial geometry in mathematics and computational g...
متن کاملEnumerating Triangulations for Products of Two Simplices and for Arbitrary Configurations of Points
We propose algorithms to enumerate (1) classes of regular triangulations in respect of symmetry for products of two simplices and (2) all triangulations, regular or not, for arbitrary con gurations of points. There are many results for triangulations in two dimension, but little is known for higher dimensions. Both objects we enumerate in this paper are for general dimensions. Products of two s...
متن کاملModuli space intersection duality between Regge surfaces and 2D dynamical triangulations
Deformation theory for 2-dimensional dynamical triangulations with N0 vertices is discussed by exploiting the geometry of the moduli space of Euclidean polygons. Such an analysis provides an explicit connection among Regge surfaces, dynamical triangulations theory and the Witten-Kontsevich model. In particular we show that a natural set of Regge measures and a triangulation counting of relevanc...
متن کاملA Polynomial Invariant and Duality for Triangulations
The Tutte polynomial TG(X,Y ) of a graph G is a classical invariant, important in combinatorics and statistical mechanics. An essential feature of the Tutte polynomial is the duality for planar graphs G, TG(X,Y ) = TG∗(Y,X) where G ∗ denotes the dual graph. We examine this property from the perspective of manifold topology, formulating polynomial invariants for higher-dimensional simplicial com...
متن کامل