论文标题
Coxeter系统具有$ 2 $维的戴维斯综合体，增长率和Perron数字
Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers
论文作者
论文摘要
在本文中，我们研究了Coxeter Systems的增长率，其中戴维斯综合体的尺寸最多为$ 2 $。我们表明，如果Coxeter系统神经的Euler特征$χ$正在消失（分别为正），那么其增长率就是塞勒姆（分别为a PISOT）数字。这样，我们由于弗洛伊德和帕里而扩大结果。此外，在$χ$为负的情况下，我们提供了无限的许多非纤维Coxeter系统，其增长率为Perron数字。
In this paper, we study growth rates of Coxeter systems with Davis complexes of dimension at most $2$. We show that if the Euler characteristic $χ$ of the nerve of a Coxeter system is vanishing (resp. positive), then its growth rate is a Salem (resp. a Pisot) number. In this way, we extend results due to Floyd and Parry. Moreover, in the case where $χ$ is negative, we provide infinitely many non-hyperbolic Coxeter systems whose growth rates are Perron numbers.
