4 citations · 12 across the 11 of their papers we have counts for
11 papers
Riordan array representation of recursive polynomial sequences, orthogonal polynomial sequences, and -orthogonal polynomial sequences
Tian-Xiao He
We study when a polynomial sequence satisfying a linear homogeneous recurrence with polynomial coefficients admits an ordinary Riordan array as its coefficient matrix.…
Divisibility of the Sums of the Power of Consecutive Integers
Tian-Xiao He, Peter J. -S. Shiue
We study the divisibility of the sums of the odd power of consecutive integers, and for odd integers and , by using…
The Vertical Recursive Relation of Riordan Arrays and Their Matrix Representation
Tian-Xiao He
A vertical recursive relation approach to Riordan arrays is induced, while the horizontal recursive relation is represented by - and -sequences. This vertical recursive appro…
On the Solutions of Three Variable Frobenius Related Problems Using Order Reduction Approach
Tian-Xiao He, Peter J. -S. Shiue, Rama Venkat
This paper presents a new approach to determine the number of solutions of three variable Frobenius related problems and to find their solutions by using order reducing methods. He…
Centralizers of the Riordan Group
Tian-Xiao He, Yuanziyi Zhang
In this paper, we discuss centralizers in the Riordan group. We will see that Faà di Bruno's formula is an application of the Fundamental Theorem of Riordan arrays. Then the compos…
One-pth Riordan Arrays in the Construction of Identities
Tian-Xiao He
For an integer we construct vertical and horizontal one-pth Riordan arrays from a Riordan array. When , one-pth Riordan arrays reduced to well known half Riordan arr…