  This paper studies the problem of constructing codes correcting deletions in
arrays. Under this model, it is assumed that an $n\times n$ array can
experience deletions of rows and columns. These deletion errors are referred to
as $(t_r,t_c)$-criss-cross deletions if $t_r$ rows and $t_c$ columns are
deleted, while a code correcting these deletion patterns is called a
$(t_r,t_c)$-criss-cross deletion correction code. The definitions for
criss-cross insertions are similar.
  It is first shown that when $t_r=t_c$ the problems of correcting criss-cross
deletions and criss-cross insertions are equivalent. The focus of this paper
lies on the case of $(1,1)$-criss-cross deletions. A non-asymptotic upper bound
on the cardinality of $(1,1)$-criss-cross deletion correction codes is shown
which assures that the redundancy is at least $2n-3+2\log n$ bits. A code
construction with an existential encoding and an explicit decoding algorithm is
presented. The redundancy of the construction is at most $2n+4 \log n + 7 +2
\log e$. A construction with explicit encoder and decoder is presented. The
explicit encoder adds an extra $5\log n + 5$ bits of redundancy to the
construction.
