论文标题
许多常规的三角形和许多多面体
Many regular triangulations and many polytopes
论文作者
论文摘要
我们表明，对于固定的$ d> 3 $和$ n $生长到无穷大，至少有$（n！）^{d-2 \ pm o（1）} $不同的标记的组合类型的$ d $ - polytopes，带有$ n $ vertices。这大约是以前最佳下限的平方。作为中间步骤，我们表明某些邻居多型（例如，特定的环状多型实现）至少具有$（n！）^{\ lfloor（d-1）/2 \ rfloor \ rfloor \ pm o（1）} $常规三角构造。
We show that for fixed $d>3$ and $n$ growing to infinity there are at least $(n!)^{d-2 \pm o(1)}$ different labeled combinatorial types of $d$-polytopes with $n$ vertices. This is about the square of the previous best lower bounds. As an intermediate step, we show that certain neighborly polytopes (such as particular realizations of cyclic polytopes) have at least $(n!)^{ \lfloor(d-1)/2\rfloor \pm o(1)}$ regular triangulations.
