Half Inverse Riordan Arrays and Their Related Vertical Recurrence Relation |
| |
Authors: | Tianxiao HE |
| |
Institution: | Department of Mathematics, Illinois Wesleyan University, Bloomington, IL $61702$-$2900$, USA |
| |
Abstract: | We discuss two different procedures to study the half Riordan arrays and their inverses. One of the procedures shows that every Riordan array is the half Riordan array of a unique Riordan array. It is well known that every Riordan array has its half Riordan array. Therefore, this paper answers the converse question: Is every Riordan array the half Riordan array of some Riordan arrays? In addition, this paper shows that the vertical recurrence relation of the column entries of the half Riordan array is equivalent to the horizontal recurrence relation of the original Riordan array''s row entries. |
| |
Keywords: | Riordan array Riordan group $A$-sequence Appell subgroup Lagrange (associated) subgroup Bell subgroup hitting-time subgroup derivative subgroup |
|
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |