论文标题
枚举间隔图和$ d $ - 代表的复合物
Enumeration of interval graphs and $d$-representable complexes
论文作者
论文摘要
对于每个固定的$ d \ ge 1 $，我们获得了$ n $顶点的$ d $ simpericial复合物的渐近估计值，该复合物作为$ n $的函数。情况$ d = 1 $对应于计数间隔图，我们在这个经过充分研究的情况下也获得了新的结果。我们的结果表明，$ d $ - 代表的综合体包括一小部分$ d $ collapsible的复合体。
For each fixed $d\ge 1$, we obtain asymptotic estimates for the number of $d$-representable simplicial complexes on $n$ vertices as a function of $n$. The case $d=1$ corresponds to counting interval graphs, and we obtain new results in this well-studied case as well. Our results imply that the $d$-representable complexes comprise a vanishingly small fraction of $d$-collapsible complexes.
