Abstract
Many combinatorial numbers can be placed in the following generalized triangular array [Tn,k]n,k≥0 satisfying the recurrence relation:Tn,k=λ(a0n+a1k+a2)Tn−1,k+(b0n+b1k+b2)Tn−1,k−1+d(da1−b1)λ(n−k+1)Tn−1,k−2 with T0,0=1 and Tn,k=0 unless 0≤k≤n for suitable a0,a1,a2,b0,b1,b2,d and λ. For n≥0, denote by Tn(q) the generating function of the n-th row. In this paper, we develop various criteria for x-Stieltjes moment property and 3-x-log-convexity of Tn(q) based on the Jacobi continued fraction expression of ∑n≥0Tn(q)tn, where x is a set of indeterminates consisting of q and those parameters occurring in the recurrence relation. With the help of a criterion of Wang and Zhu (2016) [36], we show that the corresponding linear transformation of Tn,k preserves Stieltjes moment properties of sequences. Finally, we present some related examples including factorial numbers, Whitney numbers, Stirling permutations, minimax trees and peak statistics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
