Dissertation
Annihilating Operators of Extended Riordan Arrays
Washington State University
Doctor of Philosophy (PhD), Washington State University
2023
DOI:
https://doi.org/10.7273/000005096
Abstract
An array (formally, a function D:ZxZ -> F) can be thought of as a matrix that extends infinitely in all directions. Extended Riordan arrays are lower triangular arrays that can be characterized by a triple that includes a starting element and two, potentially infinite, sequences called the A- and Z-sequence. Exploiting proprieties of the A-sequence, we look at which Riordan arrays can be alternatively characterized via the use of a finite template or overlay.
We discuss operators X and Y which shift an array right by one column or up by one row, respectively. A polynomial in X and Y that annihilates D is called a "template" whereas an "overlay" is an array with finite support that contains the coefficients of a template. Our research looks at new ways in which machinery such as templates and overlays can be applied to extended Riordan arrays.
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Details
- Title
- Annihilating Operators of Extended Riordan Arrays
- Creators
- Jessica Dickson
- Contributors
- Matthew Hudelson (Advisor)Judith McDonald (Committee Member)Michael Tsatsomeros (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 109
- Identifiers
- 99901019936901842
- Language
- English
- Resource Type
- Dissertation