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Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

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March 28, Monday, 4:10 - 5:00 PM

Jessica Dickson

Department of Mathematics and Statistics

Washington State University

Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

Zoom

March 28, Monday, 4:10 - 5:00 PM

Jessica Dickson

Department of Mathematics and Statistics

Washington State University

Title: The
Overlays of Riordan Arrays

Abstract: 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.

Abstract: 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.