Kaleidoscopical Configurations in $G$-Spaces
Kaleidoscopical Configurations in $G$-Spaces
Let $G$ be a group and $X$ be a $G$-space with the action $G\times X\rightarrow X$, $(g,x)\mapsto gx$. A subset $F$ of $X$ is called a kaleidoscopical configuration if there exists a coloring $\chi:X\rightarrow C$ such that the restriction of $\chi$ on each subset $gF$, $g\in G$, is a bijection. …