Lonesum decomposable matrices

A lonesum matrix is a (0,1)-matrix that is uniquely determined by its row and column sum vectors. In this paper, we introduce lonesum decomposable matrices and study their properties. We provide a necessary and sufficient condition for a matrix A to be lonesum decomposable, and give a generating function for the number Dk(m,n) of m×n lonesum decomposable matrices of order k. Moreover, by using this generating function we prove some congruences for Dk(m,n) modulo a prime.