On the combinatorics of extensions of preinjective Kronecker modules

We explore the combinatorial properties of a particular type of extension monoid product of preinjective Kronecker modules. The considered extension monoid product plays an important role in matrix completion problems. We state theorems which characterize this product in both implicit and explicit ways and we prove that the conditions given in the definition of the generalized majorization are equivalent with our criteria. Generalized majorization is a purely combinatorial construction introduced by its authors in a different setting.