论文标题
局部紧凑置换组的不对称着色
Asymmetric colouring of locally compact permutation groups
论文作者
论文摘要
令$ g \ leq \ mathrm {sym}（x）$，对于可计数$ x $。如果身份是$ g $保留所有颜色的唯一元素，则调用$ x $不对称的着色。 $ g $的运动（也称为最小度）是g \ setminus \ {\ mathrm {id} \} $中元素$ g \移动的元素数量的最小数量。我们表明，每个本地紧凑的，无限动作的封闭置换组都承认不对称$ 2 $颜色。这概括了Babai的最新结果，并确认了2015年Imrich，Smith，Tucker和Watkins的猜想。
Let $G \leq \mathrm{Sym} (X)$ for a countable set $X$. Call a colouring of $X$ asymmetric, if the identity is the only element of $G$ which preserves all colours. The motion (also called minimal degree) of $G$ is the minimal number of elements moved by an element $g \in G \setminus\{\mathrm{id}\}$. We show that every locally compact, closed permutation group with infinite motion admits an asymmetric $2$-colouring. This generalises a recent result by Babai and confirms a conjecture by Imrich, Smith, Tucker, and Watkins from 2015.
