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

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 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...

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

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...

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

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...

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...

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

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...

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

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...

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...

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...

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...

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

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...

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

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...

sets as its vertices. An abstract simplicial complex is a combinatorial abstraction of the notion of a simplicial complex, a shape formed by unions of line...