Recurrence Relations for the Linear Transformation Preserving the Strong $q$-Log-Convexity

[摘要] 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)

[学科分类] 离散数学和组合数学

[关键词] Strong $q$-log-convexity;Linear transformations;Recurrence relation;Stirling numbers;Whitney numbers