Collapsibility and Vanishing of Top Homology in Random Simplicial Complexes

@article{Aronshtam2013CollapsibilityAV,
  title={Collapsibility and Vanishing of Top Homology in Random Simplicial Complexes},
  author={Lior Aronshtam and Nathan Linial and Tomasz Luczak and Roy Meshulam},
  journal={Discrete & Computational Geometry},
  year={2013},
  volume={49},
  pages={317-334}
}
Let n−1 denote the (n − 1)-dimensional simplex. Let Y be a random d-dimensional subcomplex of n−1 obtained by starting with the full (d − 1)dimensional skeleton of n−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 = (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 ∂ d+1, the boundary of a (d + 1)-dimensional simplex… CONTINUE READING
Highly Cited
This paper has 24 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-7 of 7 references

Enumerative combinatorics

R. P. Stanley
Cambridge Studies in Advanced Mathematics, vol. 1, 2nd edn. Cambridge University Press, Cambridge • 2012
View 1 Excerpt

Kappeler , Topology of Random 2Complexes , Discrete Comput

D. Cohen, A. Costa, M. Farber, T.
Geom . • 2012

Topology of Random 2-Complexes

Discrete & Computational Geometry • 2012
View 1 Excerpt

The Probablistic Method

SODA '92 • 2000
View 2 Excerpts

Similar Papers

Loading similar papers…