Poset Matrix Structure Via Partial Composition Operations

This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of poset matrices of any given size by extending the combinatorial setting of species of structures to poset matrices. More specifically, three new partial composition operations that apply to poset matrices are defined as the foundation for this study. Several new structural properties derived from viewing any poset matrix and its dual in terms of these operations are highlighted.