  In this paper we give a novel solution to a classical completion problem for
square matrices. This problem was studied by many authors through time, and it
is completely solved in [2, 3]. In this paper we relate this classical problem
to a purely combinatorial question involving partitions of integers and their
majorizations studied in [4]. We show surprising relations in these approaches
and as a corollary, we obtain a new combinatorial result on partitions of
integers.
