论文标题
紧凑型双曲coxeter多面体的lannér图和组合特性
Lannér diagrams and combinatorial properties of compact hyperbolic Coxeter polytopes
论文作者
论文摘要
在本文中，我们研究了lannér图的$ \ times_0 $ - 产品。我们证明，至少有至少一个订单图$ \ ge 3 $的每个$ \ times_0 $ - 至少四个lannér图的产品都是超质的。作为推论，我们获得已知的分类耗尽所有紧凑的双曲线coxeter多型，它们在组合上等效于简单的产品。 我们还考虑紧凑的双曲线高潮型综合电脑，其每个lannér子都有订单$ 2 $。本文的第二个结果稍微改善了伯克罗夫（Burcroff）在此类多型的尺寸上的上限提高到$ 12 $。
In this paper we study $\times_0$-products of Lannér diagrams. We prove that every $\times_0$-product of at least four Lannér diagrams with at least one diagram of order $\ge 3$ is superhyperbolic. As a corollary, we obtain that known classifications exhaust all compact hyperbolic Coxeter polytopes that are combinatorially equivalent to products of simplices. We also consider compact hyperbolic Coxeter polytopes whose every Lannér subdiagram has order $2$. The second result of this paper slightly improves recent Burcroff's upper bound on the dimension of such polytopes to $12$.
