Combinatorics Algebraic combinatorics Concept
Simplicial complex
Summary
An abstract simplicial complex is a family of finite sets closed under taking subsets. Each set of size stands for a -dimensional simplex: a point, a segment, a triangle, a tetrahedron, and so on. Simplicial complexes describe spaces by finite combinatorial data, and they link combinatorics with topology and commutative algebra through f-vectors and h-vectors, homology and Stanley–Reisner rings.
Where this leads
27 pages build on this one.
- g-theorem
- Dehn–Sommerville equations
- Barycentric subdivision
- Triangulability of analytic sets
- Building
- Hauptvermutung
- f-vector and h-vector
- Order complex
- Persistent homology
- Upper bound theorem
- Euler's formula for polytopes
- Lefschetz fixed-point theorem
- Curve complex
- Sperner's lemma
- Triangulation conjecture
- Brouwer fixed-point theorem
- Nerve of a cover
- Tucker's lemma
- Mesh generation
- Triangulation
- Simplicial homology
- n-skeleton
- f-vector
- Topological data analysis
- Equivariant index theorem
- Simplicial approximation theorem
- G-signature theorem
Further reading
About this page
| Tag | V8GZ0W1ZZ5 |
|---|---|
| URI | m2://V8GZ0W1ZZ5 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 05E45, 55U10 |
| Same as |
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What links here
Used by
- Dehn–Sommerville equations
- Barycentric subdivision
- Triangulability of analytic sets
- Building
- Hauptvermutung
- f-vector and h-vector
- Order complex
- Persistent homology
- Lefschetz fixed-point theorem
- Curve complex
- Sperner's lemma
- Triangulation conjecture
- Nerve of a cover
- Tucker's lemma
- Mesh generation
- Triangulation
- Simplicial homology
- n-skeleton
- f-vector
- Topological data analysis
- Simplicial approximation theorem