Structural properties of Riordan matrices and extending the matrices

DOI10.1016/j.laa.2011.04.001zbMath1226.05021OpenAlexW2062538272WikidataQ60692256 ScholiaQ60692256MaRDI QIDQ551325

Sung-Tae Jin, Gi-Sang Cheon

Publication date: 15 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.laa.2011.04.001

zbMATH Keywords

extended Riordan matrix\((a, b)\)-sequencecompanion sequenceRiordan matrix \(A\)-sequence

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Special sequences and polynomials (11B83)

Related Items (23)

Unnamed Item ⋮ Unnamed Item ⋮ Double parameter recurrences for polynomials in bi-infinite Riordan matrices and some derived identities ⋮ Profiles of ordered trees with mutation and associated Riordan matrices ⋮ Finite and infinite dimensional Lie group structures on Riordan groups ⋮ A formula to construct all involutions in Riordan matrix groups ⋮ Some new binomial sums related to the Catalan triangle ⋮ Some algebraic structure of the Riordan group ⋮ The elements of finite order in the Riordan group over the complex field ⋮ Identities induced by Riordan arrays ⋮ Complementary Riordan arrays ⋮ Matrix characterizations of Riordan arrays ⋮ The Vertical Recursive Relation of Riordan Arrays and Their Matrix Representation ⋮ On pseudo-involutions, involutions and quasi-involutions in the group of almost Riordan arrays ⋮ Riordan posets and associated incidence matrices ⋮ Riordan graphs I: structural properties ⋮ Numerator polynomials of Riordan matrices and generalized Lagrange series ⋮ A combinatorial equivalence relation for formal power series ⋮ Some inverse limit approaches to the Riordan group ⋮ Algebraic properties of Riordan subgroups ⋮ Enumerations of rational non-decreasing Dyck paths with integer slope ⋮ The group generated by Riordan involutions ⋮ Riordan array approach to Lagrange inversion formulas and Chung-Feller theory

Uses Software

• OEIS

Cites Work

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• Combinatorial sums and implicit Riordan arrays
• Riordan matrices in the reciprocation of quadratic polynomials
• Riordan group involutions and the \(\varDelta \)-sequence
• Sequence characterization of Riordan arrays
• The Riordan group
• Riordan arrays and combinatorial sums
• Bijections and the Riordan group
• Simple proofs of open problems about the structure of involutions in the Riordan group
• Riordan group involutions
• On Some Alternative Characterizations of Riordan Arrays

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