Topology of random d-clique complexes
Topology of random d-clique complexes
复制标题
随机 d-clique 复合体的拓扑
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Demet Taylan
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文献类型：
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作者：
Demet Taylan
对于单纯复形$X$，$d$-团复形$Delta_d(X)$是以$(d+1)$-子集包含在$X$中的顶点的所有子集为面的单纯复形。我们证明了：如果$p=n^{α}$，其中$αfrac{-1}{inom{2k+2}{d}}$，则随机$d$-团复形$Delta_d(G_d(n，p))$的$k$次约化同调群几乎必然为零，且如果$frac{-1}{t}<；α<；Frc{-1}{t+1}$其中$t=(frac{(d+1)(k+1)}{inom{(d+1)(k+1)}{d+1}-(k+1)})^{-1}$，，则$Delta_d(G_d(n，p))$的$(kd+d-1)$-st约化同调群几乎必然渐近不为零。这部分回答了Eric Babson提出的一个问题。
For a simplicial complex $X$, the $d$-clique complex $Delta_d(X)$ is the simplicial complex having all subsets of vertices whose $(d + 1)$-subsets are contained by $X$ as its faces. We prove that if $p = n^{alpha}$, with $alpha frac{-1}{inom{2k+2}{d}}$, then the $k$-th reduced homology group of the random $d$-clique complex $Delta_d(G_d(n,p))$ is asymptotically almost surely vanishing, and if $frac{-1}{t} < alpha < frac{-1}{t+1}$ where $t = (frac{(d+1)(k+1)}{inom{(d+1)(k+1)}{d+1}-(k+1)})^{-1}$, then the $(kd + d -1)$-st reduced homology group of $Delta_d(G_d(n,p))$ is asymptotically almost surely nonvanishing. This provides a partial answer to a question posed by Eric Babson.
影响因子：
0.8
作者：
Costa A
通讯作者：
Costa A