Abstract
This paper introduces a new class of partially ordered sets represented as binary Riordan matrices referred to as ‘Riordan posets’. This notion extends the theory of Riordan matrices into the domain of poset theory. We establish the criterion for a given binary Riordan matrix to be defined as a Riordan poset matrix. It is also shown that every Riordan poset is a locally finite poset. This leads to the construction of various matrix algebras obtained from incidence algebras of Riordan posets. Many structural properties of Riordan posets are studied and various families of Riordan posets are introduced. A class of series-parallel posets is derived by extending the notion of Riordan posets to include exponential Riordan matrices, and it is obtained from Sheffer sequences of classical orthogonal polynomials.
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