Recurrence relations for the linear transformation preserving the strong \(q\)-log-convexity
type: Item
instance of: scholarly article
title: Recurrence relations for the linear transformation preserving the strong \(q\)-log-convexity
zbMATH Open document ID: 1344.05024
author: Lily Li Liu
author: Yanan Li
published in: The Electronic Journal of Combinatorics
publication date: 2016-09-13T00:00:00Z
full work available at URL: v23i3p44
review text: Summary: Let \([T(n,k)]_{n,k\geqslant 0}\) be a triangle of positive numbers~satisfying the three-term recurrence relation \[ T(n,k)=(a_1n+a_2k+a_3)T(n-1,k)+(b_1n+b_2k+b_3)T(n-1,k-1). \] In this paper, we give a new sufficient condition for linear transformations \[ Z_n(q)=\sum_{k=0}^{n}T(n,k)X_k(q) \] that preserves the strong \(q\)-log-convexity of polynomials sequences. As applications, we show linear transformations, given by matrices of the binomial coefficients, the Stirling numbers of the first kind and second kind, the Whitney numbers of the first kind and second kind, preserving the strong \(q\)-log-convexity in a unified manner.
Mathematics Subject Classification ID: 05A20
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 6626808
zbMATH Keywords: strong \(q\)-log-convexity
zbMATH Keywords: linear transformations
zbMATH Keywords: recurrence relation
zbMATH Keywords: Stirling numbers
zbMATH Keywords: Whitney numbers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6626808