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Everything about Abstract simplicial complex
Mathematical object
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 subsets, i.e., every subset of a set in the family is also in the family. It is a purely combinatorial description of the geometric notion of a simplicial complex. For example, in a 2-dimensional simplicial complex, the sets in the family are the triangles, their edges, and their vertices. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Abstract simplicial complexA 5-minute orientation
- Pick up a classic book: Polytopes and Discrete GeometryThe most-reprinted book on the subject
- Read the landmark paper: The Implementation of the Colored Abstract Simplicial Complex and Its Application to Mesh GenerationCited 7 times
- Go sideways: Simplicial setA closely related topic
- Go sideways: Simplicial complexA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Implementation of the Colored Abstract Simplicial Complex and Its Application to Mesh Generation
Discrete relations on abstract simplicial complexes
Simplicial intersection chains for an abstract complex
Abstract Simplicial Complexes
Monomial Polarization and Depolarization of Abstract Simplicial Complexes
Abstract simplicial complexes in Macaulay2
Compression with wildcards: Abstract simplicial complexes
$f$-vectors of subdivided simplicial complexes (extended abstract)
đź“š Books worth reading
- 📕Polytopes and Discrete GeometryGabriel Cunningham, Mark Mixer · 2021
- 📕Topics in Hyperplane ArrangementsMarcelo Aguiar, Swapneel Mahajan · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
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