Graduation Year
2009
Document Type
Thesis
Degree
M.A.
Degree Granting Department
Mathematics and Statistics
Major Professor
Brian Curtin, Ph.D.
Committee Member
Mohamed Elhamdadi, Ph.D.
Committee Member
Xiang-dong Hou, Ph.D.
Committee Member
Stephen Suen, Ph.D.
Keywords
Leonard pairs, Antiautomorphisms, Valid sequence, Simplicial complex, Hamming association scheme
Abstract
Let V denote a vector space of finite positive dimension. An ordered triple of linear operators on V is said to be a Leonard triple whenever for each choice of element of the triple there exists a basis of V with respect to which the matrix representing the chosen element is diagonal and the matrices representing the other two elements are irreducible tridiagonal. A Leonard triple is said to be modular whenever for each choice of element there exists an antiautomorphism of End(V) which fixes the chosen element and swaps the other two elements. We study combinatorial structures associated with Leonard triples and modular Leonard triples. In the first part we construct a simplicial complex of Leonard triples. The simplicial complex of a Leonard triple is the smallest set of linear operators which contains the given Leonard triple with the property that if two elements of the set are part of a Leonard triple, then the third element of the triple is also in the set. In the second part we construct a Hamming association scheme from modular Leonard triples using a method used previously in the context of Grassmanian codes.
Scholar Commons Citation
Sobkowiak, Jessica, "Some Combinatorial Structures Constructed from Modular Leonard Triples" (2009). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/27
