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Poset Matrix Structure Via Partial Composition Operations

Arnauld Mesinga Mwafise
Dec 2022
摘要
This paper examines the structure of poset matrices by formulating a set ofnew construction rules for this purpose. In this direction, the technique ofpartial composition operations will be introduced as the basis for therecursive construction of poset matrices for any given size by extending thecombinatorial setting of species of structures to poset matrices. Morespecifically, three new partial composition operation techniques that apply toposet matrices will be defined as the foundation for this study. Some keystructural patterns arising from viewing any poset matrices in terms of partialcomposition operations will be highlighted in the context of the formation ofdistinct poset matrices. The relevance of this study will set the basis formodeling the operad structure of poset matrices and their algorithmicenumeration.
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