UV-compression
= UV-compression
{c}
{title2=$C_{U,V}$}
Let $U,V\subseteq[n]$ be disjoint and have the same <cardinality>. For a set $A$, its $UV$-compression is
$$
C_{U,V}(A)=
\begin{cases}
(A\setminus V)\cup U,&A\cap(U\cup V)=V,\\
A,&\text{otherwise}.
\end{cases}
$$
For a <uniform set family> $\mathcal A$, a member is replaced only when its image is absent from $\mathcal A$; this convention preserves the family's cardinality.