Double parameter recurrences for polynomials in bi-infinite Riordan matrices and some derived identities

DOI10.1016/j.laa.2016.09.020zbMath1347.05004OpenAlexW2519375431MaRDI QIDQ331170

José L. Ramírez, Ana Luzón, Manuel Alonso-Morón

Publication date: 26 October 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2016.09.020

zbMATH Keywords

combinatorial identitiesFibonacci sequenceRiordan matrixrecurrences relations

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Combinatorics in computer science (68R05) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (5)

Exponential-type extended Riordan arrays and reciprocity law for generalized Stirling numbers ⋮ Representation of doubly infinite matrices as non-commutative Laurent series ⋮ On Ward's differential calculus, Riordan matrices and Sheffer polynomials ⋮ Riordan arrays and related polynomial sequences ⋮ The group generated by Riordan involutions

Cites Work

• Some identities of the \(r\)-Whitney numbers
• Combinatorial sums through Riordan arrays
• On convolved generalized Fibonacci and Lucas polynomials
• Structural properties of Riordan matrices and extending the matrices
• Iterative processes related to Riordan arrays: the reciprocation and the inversion of power series
• Riordan arrays and harmonic number identities
• Incomplete Fibonacci and Lucas \(p\)-numbers
• Identities induced by Riordan arrays
• Incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers
• Ultrametrics, Banach's fixed point theorem and the Riordan group
• Riordan matrices in the reciprocation of quadratic polynomials
• A generalization of Lucas polynomial sequence
• The Riordan group
• Pascal triangles, Catalan numbers and renewal arrays
• Riordan arrays and combinatorial sums
• Generating functions of the incomplete Fibonacci and Lucas numbers
• Some identities related to reciprocal functions
• Riordan arrays and the Abel-Gould identity
• Incomplete Fibonacci and Lucas numbers
• Determinant representations of polynomial sequences of Riordan type
• Generalized Fibonacci polynomials and fibonomial coefficients
• Representing polynomials as characteristic polynomials via the Stieltjes transform
• Complementary Riordan arrays
• Generalized harmonic numbers with Riordan arrays
• Negation of binomial coefficients
• Some results on convolved (p,q)-Fibonacci polynomials
• Recurrence relations for polynomial sequences via Riordan matrices
• Some inverse limit approaches to the Riordan group
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