Row sums and alternating sums of Riordan arrays

DOI10.1016/j.laa.2016.05.035zbMath1343.05022OpenAlexW2416771097MaRDI QIDQ306429

F. Blanchet-Sadri, M. Dambrine

Publication date: 31 August 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.2016.05.035

zbMATH Keywords

Riordan groupBell subgroupRiordan arraysAppell subgroupassociate subgroupcheckerboard subgroupderivative subgroupGirard-Waring type identitieshitting-time subgrouprow sum functions and alternating row sum functions of Riordan arrays

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05) Special sequences and polynomials (11B83) Matrices of integers (15B36) Linear equations (linear algebraic aspects) (15A06) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items

A note on Eulerian numbers and Toeplitz matrices ⋮ Applications of Riordan matrix functions to Bernoulli and Euler polynomials ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fuss-Catalan matrices, their weighted sums, and stabilizer subgroups of the Riordan group ⋮ Summations on the diagonals of a Riordan array and some applications ⋮ The halves of a 3-dimensional Riordan array ⋮ The skew halves of a Riordan array ⋮ Row polynomial matrices of Riordan arrays ⋮ Riordan graphs I: structural properties ⋮ A unified approach for the Catalan matrices by using Riordan arrays ⋮ Identities for linear recursive sequences of order 2 ⋮ Recursive sequences and Girard-Waring identities with applications in sequence transformation

Uses Software

• OEIS

Cites Work

• Combinatorics of Riordan arrays with identical \(A\) and \(Z\) sequences
• Matrix characterizations of Riordan arrays
• A symbolic operator approach to several summation formulas for power series. II
• On sequences of numbers and polynomials defined by linear recurrence relations of order 2
• Sequence characterization of Riordan arrays
• The Riordan group
• Pascal triangles, Catalan numbers and renewal arrays
• Bijections and the Riordan group
• A divisibility property for a subgroup of Riordan matrices
• Inverse series relations and other expansions involving Humbert polynomials
• On Some Alternative Characterizations of Riordan Arrays
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item