Geodesic
Recurrence relations for the linear transformation preserving the strong \(q\)-log-convexity
Lily Li Liu1 ; Ya-Nan Li1
1Qufu Normal University
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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Let $[T(n,k)]_{n,k\geqslant0}$ 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.
DOI : 10.37236/5913
Classification : 05A20, 11B73, 11B37
Mots-clés : strong \(q\)-log-convexity, linear transformations, recurrence relation, Stirling numbers, Whitney numbers

Lily Li Liu  1   ; Ya-Nan Li  1

1 Qufu Normal University 
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     author = {Lily Li Liu and Ya-Nan Li},
     title = {Recurrence relations for the linear transformation preserving the strong \(q\)-log-convexity},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {3},
     doi = {10.37236/5913},
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Lily Li Liu; Ya-Nan Li. Recurrence relations for the linear transformation preserving the strong \(q\)-log-convexity. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/5913

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