  Lonesum matrices are matrices that are uniquely reconstructible from their
row and column sum vectors. These matrices are enumerated by the poly-Bernoulli
numbers that are related to the multiple zeta values and have a rich literature
in number theory. Combinatorially, lonesum matrices are in bijection with many
other combinatorial objects: several permutation classes, other matrix classes,
acyclic orientations in graphs etc. Motivated of these facts, we study in this
paper lonesum matrices with restriction on the number of columns and rows of
the same type.
