#### Graduation Year

2008

#### Document Type

Dissertation

#### Degree

Ph.D.

#### Degree Granting Department

Mathematics and Statistics

#### Major Professor

Brian Curtin, Ph.D.

#### Committee Member

Masahiko Saito, Ph.D.

#### Committee Member

Xiang-dong Hou, Ph.D.

#### Committee Member

Brendan T. Nagle, Ph.D.

#### Keywords

Terwilliger algebra, Bose-Mesner algebra, Association scheme, Strongly regular graph, Fusions

#### Abstract

Let *n* be a positive integer. A *Latin square of order n* is an n×n array *L* such that each element of some *n*-set occurs in each row and in each column of *L* exactly once. It is well-known that one may construct a 4-class association scheme on the positions of a Latin square, where the relations are the identity, being in the same row, being in the same column, having the same entry, and everything else. We describe the subconstituent (Terwilliger) algebras of such an association scheme. One also may construct several strongly regular graphs on the positions of a Latin square, where adjacency corresponds to any subset of the nonidentity relations described above. We describe the local spectrum and subconstituent algebras of such strongly regular graphs. Finally, we study various notions of isomorphism for subconstituent algebras using Latin squares as examples.

#### Scholar Commons Citation

Daqqa, Ibtisam, "Subconstituent Algebras of Latin Squares" (2007). *Graduate Theses and Dissertations.*

https://digitalcommons.usf.edu/etd/199