We find an upper bound on the reflection or absolute length of Coxeter group elements as a function of the number of generators and the standard length. For any universal Coxeter group, we show that there are elements which achieve the bound for any given standard length.

中文翻译：

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Coxeter组中反射长度的上限

我们发现Coxeter组元素的反射或绝对长度的上限是生成器数量和标准长度的函数。对于任何通用的Coxeter组，我们表明存在可以达到任何给定标准长度范围的元素。