Poset Matrix Structure Via Partial Composition Operations

TL;DR

This paper introduces new partial composition operations to construct and analyze poset matrices, extending combinatorial species theory to better understand their structure and properties.

Contribution

It defines three novel partial composition operations for poset matrices and explores their structural implications, advancing the combinatorial understanding of poset matrices.

Findings

Defined three new partial composition operations for poset matrices

Derived structural properties from these operations

Extended species of structures framework to poset matrices

Abstract

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.