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22,702
Progressive Simplicial Complexes
, 1997
"... In this paper, we introduce the progressive simplicial complex (PSC) representation, a new format for storing and transmitting triangulated geometric models. Like the earlier progressive mesh (PM) representation, it captures a given model as a coarse base model together with a sequence of refinement ..."
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Cited by 172 (2 self)
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In this paper, we introduce the progressive simplicial complex (PSC) representation, a new format for storing and transmitting triangulated geometric models. Like the earlier progressive mesh (PM) representation, it captures a given model as a coarse base model together with a sequence
Equivariant Simplicial Complexes Revisited
"... The traditional definition of an equivariant simplicial complex for finite groups is extended to locally compact topological groups. Definitions for both abstract and nonabstract equivariant simplicial complexes are provided, and constructions for passing between the two are given. The functorialit ..."
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Cited by 1 (0 self)
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The traditional definition of an equivariant simplicial complex for finite groups is extended to locally compact topological groups. Definitions for both abstract and nonabstract equivariant simplicial complexes are provided, and constructions for passing between the two are given
ON PTOLEMAIC METRIC SIMPLICIAL COMPLEXES
, 906
"... Abstract: We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy’s inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isomet ..."
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Abstract: We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy’s inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which
Abstract simplicial complexes
 Formalized Mathematics
"... Summary. In this article we define the notion of abstract simplicial complexes and operations on them. We introduce the following basic notions: simplex, face, vertex, degree, skeleton, subdivision and substructure, and prove some of their properties. ..."
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Cited by 2 (2 self)
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Summary. In this article we define the notion of abstract simplicial complexes and operations on them. We introduce the following basic notions: simplex, face, vertex, degree, skeleton, subdivision and substructure, and prove some of their properties.
Geometric Realization of Simplicial Complexes
"... Abstract. We show that an abstract simplicial complex \Delta may be realized on a grid of IRd \Gamma 1, where d = dim P (\Delta) is the order dimension ..."
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Abstract. We show that an abstract simplicial complex \Delta may be realized on a grid of IRd \Gamma 1, where d = dim P (\Delta) is the order dimension
FiniteResolution Simplicial Complexes
, 1998
"... Simplicial Complexes are used to model topology in Geographic Information Systems (GIS). Line intersection is an essential operation to update them. We introduce a finiteresolution line intersection method, called Zero Order Intersection, and apply it to simplicial complexes. Any reliable implemen ..."
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Simplicial Complexes are used to model topology in Geographic Information Systems (GIS). Line intersection is an essential operation to update them. We introduce a finiteresolution line intersection method, called Zero Order Intersection, and apply it to simplicial complexes. Any reliable
Duality theorems for simplicial complexes
, 2011
"... This thesis deals with the homology and cohomology groups of simplicial complexes, and especially with the two duality theorems which will demonstrate links between the two notions. For this we will need some results, and we will therefore prove the long exact sequence for the reduced relative homol ..."
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This thesis deals with the homology and cohomology groups of simplicial complexes, and especially with the two duality theorems which will demonstrate links between the two notions. For this we will need some results, and we will therefore prove the long exact sequence for the reduced relative
The infinite random simplicial complex
, 2013
"... We study the Fräısse ́ limit of the class of all finite simplicial complexes. Whilst the natural modeltheoretic setting for this class uses an infinite language, a range of results associated with Fräısse ́ limits of structures for finite languages carry across to this important example. We intr ..."
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We study the Fräısse ́ limit of the class of all finite simplicial complexes. Whilst the natural modeltheoretic setting for this class uses an infinite language, a range of results associated with Fräısse ́ limits of structures for finite languages carry across to this important example. We
Exponential random simplicial complexes
, 2015
"... Exponential random graph models have attracted significant research attention over the past decades. These models are maximumentropy ensembles subject to the constraints that the expected values of a set of graph observables are equal to given values. Here we extend these maximumentropy ensembles ..."
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to random simplicial complexes, which are more adequate and versatile constructions to model complex systems in many applications. We show that many random simplicial complex models considered in the literature can be casted as maximumentropy ensembles under certain constraints. We introduce and analyze
Glicci simplicial complexes
"... ABSTRACT. One of the main open questions in liaison theory is whether every homogeneous CohenMacaulay ideal in a polynomial ring is glicci, i.e. if it is in the Gliaison class of a complete intersection. We give an affirmative answer to this question for StanleyReisner ideals defined by simplicia ..."
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Cited by 9 (4 self)
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by simplicial complexes that are weakly vertexdecomposable. This class of complexes includes matroid, shifted and Gorenstein complexes respectively. Moreover, we construct a simplicial complex which shows that the property of being glicci depends on the characteristic of the base field. As an application
Results 1  10
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22,702