Abstract
Several years ago Linial and Meshulam (Combinatorica 26 (2006) 457-487) introduced a model called Xd(n,p) of random n-vertex d-dimensional simplicial complexes. The following question suggests itself very naturally: What is the threshold probability p=p(n) at which the d-dimensional homology of such a random d-complex is, almost surely, nonzero? Here we derive an upper bound on this threshold. Computer experiments that we have conducted suggest that this bound may coincide with the actual threshold, but this remains an open question.
| Original language | English |
|---|---|
| Pages (from-to) | 26-35 |
| Number of pages | 10 |
| Journal | Random Structures and Algorithms |
| Volume | 46 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2015 |
Bibliographical note
Publisher Copyright:© 2013 Wiley Periodicals, Inc.
Keywords
- Collapsibility
- Homology
- Random simplicial complex
- Threshold
- Topology