Title: Riordan Arrays: From infinite A-sequences to finite Templates
 
Abstract: A Riordan Array can be thought of as lower triangular matrix that extends infinitely downwards and to the right. A Riordan Array is traditionally characterized by two generating functions, but it can also be defined using A- and Z-sequences. These sequences impose a specific pattern to a Riordan Array’s rows and the sequences themselves may either terminate at some index or continue indefinitely.
     In this talk we explore representing A-sequences in a finite form via the use of “Templates.” A Template is a polynomial in X and Y where X and Y are considered operators that shift an array either right by one column or up by one row, respectively. We will show that by using these operators we are able to give an alternative, often finite, method of expressing A-sequences.