Deletion-correcting codes and dominant vectors

In this paper we describe all pairs of binary vectors $(\mathbf{u},\mathbf{v})$ such that the set of vectors obtained by $t$ deletions in $\mathbf{v}$ is a subset of the set of vectors obtained by $t$ deletions in $\mathbf{u}$ 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 $n$.