论文标题
shot弹枪组装
Shotgun Assembly of Linial-Meshulam Model
论文作者
论文摘要
In a recent paper [6], J. Gaudio and E. Mossel studied the shotgun assembly of the Erdős-Rényi graph $\mathcal G(n,p_n)$ with $p_n=n^{-α}$, and showed that the graph is reconstructable form its $1$-neighbourhoods if $0<α< 1/3$ and not reconstructable from its $ 1 $ -Neighbourhoods如果$ 1/2 <α<1 $。在本文中，我们将图形重建的概念推广到简单复合物的重建。我们表明，$ n $顶点上的$ n $顶点上的外线 - 壳模型$ y_ {d}（n，p_n）$，$ p_n = n^{ - α} $可以从$ 1 $ -nighbourhoods中重建$ 0 <α<1/3 $，而不是重建$ 1 $ -neighbourable的$ 1 $ -neighbourbourable $ -neighbourbourbourbourbourable。
In a recent paper [6], J. Gaudio and E. Mossel studied the shotgun assembly of the Erdős-Rényi graph $\mathcal G(n,p_n)$ with $p_n=n^{-α}$, and showed that the graph is reconstructable form its $1$-neighbourhoods if $0<α< 1/3$ and not reconstructable from its $1$-neighbourhoods if $1/2 <α<1$. In this article, we generalise the notion of reconstruction of graphs to the reconstruction of simplicial complexes. We show that the Linial-Meshulam model $Y_{d}(n,p_n)$ on $n$ vertices with $p_n=n^{-α}$ is reconstructable from its $1$-neighbourhoods when $0< α< 1/3$ and is not reconstructable form its $1$-neighbourhoods when $1/2 < α< 1$.
