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Washington State University
Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics
  March 28, Monday, 4:10 - 5:00 PM


Jessica Dickson

Department of Mathematics and Statistics
Washington State University

Title: The Overlays of Riordan Arrays
In this talk we discuss new and potential ways in which machinery such as templates and overlays can be applied to well-studied arrays, specifically Riordan arrays.
    An array can be thought of as a matrix that extends infinitely in all directions. Operators X and Y shift an array right by one column or up by one row, respectively. A polynomial in X and Y that annihilates an array is called a ``template" whereas an ``overlay" is an array with finite support that contains the coefficients of a template.
    Riordan arrays are lower triangular arrays that extend infinitely only to the right and downwards. They were originally motivated by a generalization of Pascal's triangle and can be described in one of two ways: Either column-wise by their generating functions or row-wise by their associated patterned sequence. This pattern sequence often corresponds to a natural representation as an overlay. In this talk we explore that representation and the requirements for such a representation to exist.