Notes on the total positivity of Riordan arrays

DOI10.1016/j.laa.2019.01.015zbMath1411.05030OpenAlexW2912617141MaRDI QIDQ2418981

Xi Chen, Yi Wang

Publication date: 29 May 2019

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

Full work available at URL: https://doi.org/10.1016/j.laa.2019.01.015

zbMATH Keywords

Pólya frequency sequencetotal positivityRiordan array

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial inequalities (05A20) Miscellaneous inequalities involving matrices (15A45) Special sequences and polynomials (11B83) Matrices of integers (15B36)

Related Items (12)

Proof of a conjecture on the total positivity of amazing matrices ⋮ Total positivity of some polynomial matrices that enumerate labeled trees and forests. I: Forests of rooted labeled trees ⋮ The Laguerre-Pólya class and combinatorics. Abstracts from the workshop held March 13--19, 2022 ⋮ Analytic combinatorics of coordination numbers of cubic lattices ⋮ Lattice paths and branched continued fractions. II: Multivariate Lah polynomials and Lah symmetric functions ⋮ Bijective proofs of recurrences involving two Schröder triangles ⋮ Analytic properties of combinatorial triangles related to Motzkin numbers ⋮ Riordan arrays and related polynomial sequences ⋮ Yet another criterion for the total positivity of Riordan arrays ⋮ Some (counter)examples on totally positive Riordan arrays ⋮ Analytic aspects of Delannoy numbers ⋮ Total Positivity from the Exponential Riordan Arrays

Cites Work

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• Combinatorics of Riordan arrays with identical \(A\) and \(Z\) sequences
• Identities induced by Riordan arrays
• Sequence characterization of Riordan arrays
• The Riordan group
• Riordan arrays and combinatorial sums
• Polynomials with real zeros and Pólya frequency sequences
• Combinatorics and total positivity
• Total positivity of Riordan arrays
• Total positivity of recursive matrices
• Schröder matrix as inverse of Delannoy matrix
• Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices

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