Half Inverse Riordan Arrays and Their Related Vertical Recurrence Relation
Received:January 18, 2023  Revised:April 26, 2023
Key Words: Riordan array   Riordan group   $A$-sequence   Appell subgroup   Lagrange (associated) subgroup   Bell subgroup   hitting-time subgroup   derivative subgroup  
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Author NameAffiliation
Tianxiao HE Department of Mathematics, Illinois Wesleyan University, Bloomington, IL $61702$-$2900$, USA 
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      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.
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