Name
Abstract | ||
|---|---|---|
Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplex-wise linear embedding of the triangulation into Euclidean space is ''as convex as possible''. It can thus be understood as a generalization of the concept of convexity. In even dimensions, super-neighborliness is known to be a purely combinatorial condition which implies the tightness of a triangulation. Here, we present other sufficient and purely combinatorial conditions which can be applied to the odd-dimensional case as well. One of the conditions is that all vertex links are stacked spheres, which implies that the triangulation is in Walkup@?s class K(d). We show that in any dimension d=4, tight-neighborly triangulations as defined by Lutz, Sulanke and Swartz are tight. Furthermore, triangulations with k-stacked vertex links and the centrally symmetric case are discussed. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jcta.2011.03.003 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
stacked polytopes,k-stacked vertex link,combinatorial condition,topological condition,triangulated manifold,stacked polytope,tight triangulations,tight-neighborly triangulations,euclidean space,odd-dimensional case,class k,polar morse function,tight triangulation,vertex link,symmetric case,simplex-wise linear embedding,morse function | Discrete mathematics,Combinatorics,Vertex (geometry),Stacked polytope,Triangulation,Triangulation (social science),Polytope,Mathematics,Manifold,Pitteway triangulation,Point set triangulation | Journal |
Volume | Issue | ISSN |
118 | 6 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
8 | 1.05 | 13 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Felix Effenberger | 1 | 37 | 5.94 |