Collapsibility and Vanishing of Top Homology in Random Simplicial Complexes
Authors:
- Lior Aronshtam,
- Nathan Linial,
- Tomasz Łuczak,
- Roy Meshulam
Abstract
Let Δn-1 denote the (n - 1)-dimensional simplex. Let Y be a random d-dimensional subcomplex of Δn-1 obtained by starting with the full (d - 1)-dimensional skeleton of Δn-1 and then adding each d-simplex independently with probability p = c/n. We compute an explicit constant γd, with γ2 ≃ 2. 45, γ3 ≃ 3.5, and γd = Θ (log d) as d → ∞, so that for c < γd such a random simplicial complex either collapses to a (d - 1)-dimensional subcomplex or it contains ∂ Δd+1, the boundary of a (d + 1)-dimensional simplex. We conjecture this bound to be sharp. In addition, we show that there exists a constant γd < cd < d + 1 such that for any c > cd and a fixed field F, asymptotically almost surely Hd(Y;F) ≠ 0. © 2012 Springer Science+Business Media New York.
- Record ID
- UAM369df3b89e11483c8912a2aa80a2db20
- Author
- Journal series
- Discrete & Computational Geometry, ISSN 0179-5376
- Issue year
- 2013
- Vol
- 49
- No
- 2
- Pages
- 317-334
- ASJC Classification
- ; ; ;
- DOI
- DOI:10.1007/s00454-012-9483-8 Opening in a new tab
- URL
- https://link.springer.com/article/10.1007%2Fs00454-012-9483-8 Opening in a new tab
- Language
- (en) English
- File
-
- File: 1
- Aronshtam2013_Article_CollapsibilityAndVanishingOfTo.pdf
-
- Score (nominal)
- 30
- Score source
- journalList
- Score
- Publication indicators
- = 29; = 28; = 81; : 2013 = 1.251; : 2013 (2 years) = 0.606 - 2013 (5 years) =0.723
- Citation count
- 81
Share
- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAM369df3b89e11483c8912a2aa80a2db20/
- URN
urn:amu-prod:UAM369df3b89e11483c8912a2aa80a2db20
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.