Sponsor
Portland State University. Department of Mathematics and Statistics
First Advisor
John Caughman
Term of Graduation
Spring 2024
Date of Publication
4-1-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.) in Mathematical Sciences
Department
Mathematics and Statistics
Language
English
Physical Description
1 online resource (viii, 96 pages)
Abstract
In Linear algebra, the concept of Leonard pair (LP) was motivated by the theory of Q-polynomial distance-regular graphs. In this dissertation, we will first give a brief introduction to LPs and to two closely-related classes of objects: (i) bipartite Leonard pairs (BLPs) and (ii) almost bipartite Leonard pairs (ABLPs). Taking these as departure points, we will introduce a new class of object - doubly almost bipartite Leonard pairs (DABLPs). The primary aim of our work is to fully classify (up to isomorphism) this new family. In addition, since there is known to be a natural correspondence between Leonard pairs and families of orthogonal polynomials, we reveal which families of orthogonal polynomials correspond to the DABLPs. Several related objects, such as Leonard triples, modular Leonard triples, spin Leonard pairs, and near-bipartite Leonard pairs have corresponding notions for the doubly almost bipartite case. These analogous objects are also defined and briefly explored.
Rights
© 2024 Shuichi Masuda
In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
Persistent Identifier
https://archives.pdx.edu/ds/psu/42218
Recommended Citation
Masuda, Shuichi, "Doubly Almost Bipartite Leonard Pairs" (2024). Dissertations and Theses. Paper 6611.