论文标题
二维Coxeter组为双重
2-dimensional Coxeter groups are biautomatic
论文作者
论文摘要
令$ w $为$ 2 $ - 维的coxeter组，也就是说，一个$ \ frac {1} {m_ {st}}+\ frac {1} {1} {m_ {sr}}}+\ frac {1} {1} {1} {m_ {m_ {tr}}} {m_ {tr}} \ for s $ s $我们证明$ w $是双重的。我们通过证明天然的大地语言是常规的（对于任意$ w $）来做到这一点，并满足旅行者的财产。结果，根据Jacekświątkowski的工作，在$ W $类型的建筑物上正确和共同行动的小组也是双重的。我们还表明，自然语言的旅行者属性因$ W = \ widetilde {a} _3 $而失败。
Let $W$ be a $2$-dimensional Coxeter group, that is, a one with $\frac{1}{m_{st}}+\frac{1}{m_{sr}}+\frac{1}{m_{tr}}\leq 1$ for all triples of distinct $s,t,r\in S$. We prove that $W$ is biautomatic. We do it by showing that a natural geodesic language is regular (for arbitrary $W$), and satisfies the fellow traveller property. As a consequence, by the work of Jacek Świątkowski, groups acting properly and cocompactly on buildings of type $W$ are also biautomatic. We also show that the fellow traveller property for the natural language fails for $W=\widetilde{A}_3$.
