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- W2949228196 abstract "Let Y be a random d-dimensional subcomplex of the (n-1)-dimensional simplex S obtained by starting with the full (d-1)-dimensional skeleton of S and then adding each d-simplex independently with probability p=c/n. We compute an explicit constant gamma_d=Theta(log d) so that for c < gamma_d such a random simplicial complex either collapses to a (d-1)-dimensional subcomplex or it contains the boundary of a (d+1)-simplex. We conjecture this bound to be sharp. In addition we show that there exists a constant gamma_d< c_d <d+1 such that for any c>c_d and a fixed field F, asymptotically almost surely H_d(Y;F) neq 0." @default.
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- W2949228196 date "2010-10-07" @default.
- W2949228196 modified "2023-09-27" @default.
- W2949228196 title "Collapsibility and vanishing of top homology in random simplicial complexes" @default.
- W2949228196 cites W2952519650 @default.
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- W2949228196 doi "https://doi.org/10.48550/arxiv.1010.1400" @default.
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