The link in a simplicial complex is a generalization of the neighborhood of a vertex in a graph. The link of a vertex encodes information about the local...

In mathematics, a simplicial complex is a structured set composed of points, line segments, triangles, and their n-dimensional counterparts, called simplices...

In combinatorics, an abstract simplicial complex (ASC), often called an abstract complex or just a complex, is a family of sets that is closed under taking...

subgraphs) of an undirected graph. The clique complex X(G) of an undirected graph G is an abstract simplicial complex (that is, a family of finite sets closed...

triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism. A space that admits...

a related concept in polyhedra Link (simplicial complex), a generalization of the neighborhood to simplicial complexes Hell 1978, Sedláček 1983 Wigderson...

algebraic topology and topological data analysis, the Čech complex is an abstract simplicial complex constructed from a point cloud in any metric space which...

sets Chain complex, an algebraic structure Simplicial complex, a kind of topological space CW complex, a kind of topological space Line complex, a 3-dimensional...

contexts. See: Geometric realization of an abstract simplicial complex; Geometric realization of a simplicial set; This disambiguation page lists articles associated...

tree is a type of trie used to represent efficiently any general simplicial complex. Through its nodes, this data structure notably explicitly represents...

In mathematics, the curve complex is a simplicial complex C(S) associated to a finite-type surface S, which encodes the combinatorics of simple closed...

the task easier. The simplicial homology groups Hn(X) of a simplicial complex X are defined using the simplicial chain complex C(X), with Cn(X) the free...

topological space from distances in a set of points. It is an abstract simplicial complex that can be defined from any metric space M and distance δ by forming...

simplicial complex. Link (knot theory), a collection of knots entangled with one another Link function in statistics Link (Mars), a rock outcrop Link...

illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory...

illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory...

conditions on the complexes Δ that can arise in this fashion. By treating these conditions as axioms for a class of simplicial complexes, Tits arrived at...

System In geometry, Barycentric subdivision, a way of dividing a simplicial complex Barycentric coordinates (mathematics), coordinates defined by the...

i of X ', a simplicial complex Li' endowed with a rigid simplicial action of a finite group Γi. a simplicial map φi of Li' onto the link Li of i in X...

Such ideals are described more geometrically in terms of finite simplicial complexes. The Stanley–Reisner ring construction is a basic tool within algebraic...

n-dimensional analogue of a triangle Simplicial polytope, a polytope with all simplex facets Simplicial complex, a collection of simplicies Pascal's simplex...

graph, whereby replacing the edges by paths Subdivision (simplicial complex) Subdivision (simplicial set) Subdivision surface, in computer graphics Subdivision...

a simplicial complex, its fundamental group can be described explicitly in terms of generators and relations. If X is a connected simplicial complex, an...

α-complex of the given set of points is the simplicial complex formed by the set of edges and triangles whose radii are at most 1/α. The α-complex is...

facet of a simplicial complex is a maximal simplex, that is a simplex that is not a face of another simplex of the complex. For (boundary complexes of) simplicial...

slightly different concept from the boundary of a manifold or of a simplicial complex. For example, the boundary of an open disk viewed as a manifold is...

A chessboard complex is a particular kind of abstract simplicial complex, which has various applications in topological graph theory and algebraic topology...

since it is locally Euclidean. Similarly, every simplex and every simplicial complex inherits a natural topology from Rn. The Zariski topology is defined...

normalizes generalized gamma variates, one obtains variates from the simplicial generalized beta distribution (SGB). On the other hand, SGB variates can...

example of a finite simplicial complex that is a topological manifold but not a PL manifold. (It is not a PL manifold because the link of a point is not...