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

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...

is topological properties of simplicial complexes and its generalization, cell-complexes. An abstract simplicial complex above a set V {\displaystyle...

In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of...

models like simplicial and cell complexes. Combinatorial Complexes : Generalize and bridge the gaps between simplicial complexes, cell complexes, and hypergraphs...

In mathematics, a simplicial set is an object composed of simplices in a specific way. Simplicial sets are higher-dimensional generalizations of directed...

operation on simplicial complexes. In algebraic topology it is sometimes useful to replace the original spaces with simplicial complexes via triangulations:...

combinatorial counterpart to a simplicial complex is an abstract simplicial complex. See also random geometric complexes. The discipline of combinatorial...

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

another fixed simplicial complex. The problem is undecidable for complexes of dimension 5 or more.: 9–11  An abstract simplicial complex (ASC) is family...

to develop the simplicial homology of a triangulated manifold and to create what is now called a chain complex. These chain complexes (since greatly generalized)...

refinement) of a simplicial complex is another simplicial complex in which, intuitively, one or more simplices of the original complex have been partitioned...

In mathematics, the blancmange curve is a self-affine fractal curve constructible by midpoint subdivision. It is also known as the Takagi curve, after...

theorem gives a complete characterization of the f-vectors of abstract simplicial complexes. It includes as a special case the Erdős–Ko–Rado theorem and can...

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...

n-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the...

properties than simplicial complexes, but still retains a combinatorial nature that allows for computation (often with a much smaller complex). The C stands...

A simplicial map (also called simplicial mapping) is a function between two simplicial complexes, with the property that the images of the vertices of...

between spaces that are built up from simplices—that is, finite simplicial complexes. The general continuous mapping between such spaces can be represented...

spaces called simplicial complexes. These spaces are built from simplices glued together in a combinatorial fashion. Simplicial complexes are used to define...