Riordan arrays, the A-matrix, and Somos 4 sequences

2019/12/02 by Paul Barry, Barry, Paul
Computer Science · Engineering · Mathematics · #11B37 #11B83 #11C20 #15B36 #Advanced Combinatorial Mathematics #Blind Source Separation Techniques #Combinatorics (math.CO) #FOS: Mathematics #Primary 15B36 #Secondary 05A15 #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1912.01126

openalex publication_date 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize certain Riordan arrays by their A-matrices and ρ sequences. We conjecture the form of a generic A-matrix which leads to Somos 4 sequences. We find an A-matrix that produces a Riordan quasi-involution, and we study the A-matrices and ρ sequences of the moment matrices of certain perturbed orthogonal polynomials.

Citations

• On Some Alternative Characterizations of Riordan Arrays
• The on-line encyclopedia of integer sequences

Related

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• Embedding structures associated with Riordan arrays and moment matrices
• On the partial sums of Riordan arrays
• The Vertical Recursive Relation of Riordan Arrays and Their Matrix Representation
• d-orthogonal polynomials, Fuss-Catalan matrices and lattice paths