Equidecomposable subsets under a group action
= Equidecomposable subsets under a group action
For a group $G$ acting on a set $X$, subsets $A,B\subseteq X$ are $G$-equidecomposable when there are finite partitions $A=\bigsqcup_i A_i$ and $B=\bigsqcup_i B_i$ and elements $g_i\in G$ with $g_iA_i=B_i$ for every $i$.