In mathematics, an **abstract simplicial complex** is a purely combinatorial description of the geometric notion of a simplicial complex, consisting of a family of finite sets closed under the operation of taking subsets. In the context of matroids and greedoids, abstract simplicial complexes are also called **independence systems**.

Read more about Abstract Simplicial Complex: Definitions, Geometric Realization, Examples, Enumeration

### Other articles related to "complex, simplicial, abstract simplicial complex, simplicial complex":

... The correct definition of the cotangent

**complex**begins in the homotopical setting ... Quillen and André worked with the

**simplicial**commutative rings, while Illusie worked with

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... In geometry, a

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... Let be the singular chain

**complex**functor and be the

**simplicial**chain

**complex**functor ... and -acyclic (the proof that is not entirely straigtforward and uses a detour through

**simplicial**subdivision, which can also be handled using the above theorem) ... It is rather obvious that and so we conclude that singular and

**simplicial**homology are isomorphic on ...

**Abstract Simplicial Complex**- Enumeration

... The number of abstract simplicial complexes on n elements is the nth Dedekind number ... These numbers grow very rapidly, and are known only for n ≤ 8 they are 2, 3, 6, 20, 168, 7581, 7828354, 2414682040998, 56130437228687557907788 (sequence A000372 in OEIS) ...

... An

**abstract simplicial complex**is a combinatorial abstraction of the notion of a

**simplicial complex**, a shape formed by unions of line segments, triangles ... In an

**abstract simplicial complex**, each simplex is represented simply as the set of its vertices ... also belong to the family forms an

**abstract simplicial complex**...

### Famous quotes containing the words complex and/or abstract:

“The human mind is so *complex* and things are so tangled up with each other that, to explain a blade of straw, one would have to take to pieces an entire universe.... A definition is a sack of flour compressed into a thimble.”

—Rémy De Gourmont (1858–1915)

“... my whole existence is governed by *abstract* ideas.... the ideal must be preserved regardless of fact.”

—Mary Corinna Putnam (1842–1906)