  In this paper we describe all pairs of binary vectors $({\bf u}, {\bf v})$
such that the set of vectors obtained by $t$ deletions in ${\bf v}$ is a subset
of the set of vectors obtained by $t$ deletions in ${\bf u}$ for $t=1,2$. Such
pairs play an important role for finding the value of $L_2(n,t)$, the maximum
cardinality of binary $t$-deletion-correcting code of length $n$.
