  We prove that in every cover of a Young diagram with $\binom{2k}{k}$ steps
with generalized rectangles there is a row or a column in the diagram that is
used by at least $k+1$ rectangles. We show that this is best-possible by
partitioning any Young diagram with $\binom{2k}{k}-1$ steps into actual
rectangles, each row and each column used by at most $k$ rectangles. This
answers two questions by Kim et al. (2018).
  Our results can be rephrased in terms of local covering numbers of difference
graphs with complete bipartite graphs, which has applications in the recent
notion of local dimension of partially ordered sets.
