Integral Homology of Random Simplicial Complexes
| Autor: | Tomasz Łuczak, Yuval Peled |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Probability (math.PR)
010102 general mathematics Complete graph 0102 computer and information sciences Homology (mathematics) 01 natural sciences Theoretical Computer Science Combinatorics Simplicial complex Computational Theory and Mathematics 010201 computation theory & mathematics FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Mathematics - Algebraic Topology Geometry and Topology 0101 mathematics Mathematics - Probability Mathematics |
| Zdroj: | Discrete & Computational Geometry. 59:131-142 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-017-9938-z |
| Popis: | The random 2-dimensional simplicial complex process starts with a complete graph on n vertices, and in every step a new 2-dimensional face, chosen uniformly at random, is added. We prove that with probability tending to 1 as $$n\rightarrow \infty $$ , the first homology group over $$\mathbb {Z}$$ vanishes at the very moment when all the edges are covered by triangular faces. |
| Databáze: | OpenAIRE |
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