Degree Type

Dissertation

Date of Award

2008

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Sung Yell Song

Second Advisor

Leslie Hogben

Third Advisor

Elgin Johnston

Abstract

In this thesis, we study the T -algebras of symmetric association schemes that are obtained as the wreath product of H(1, m) for m ≥ 2. We find that the D-class association scheme Kn1&m22;Kn2&m22;&cdots; &m22;KnD formed by taking the wreath product of one-class association schemes Kni = H(1, ni) has the triple-regularity property. We determine the dimension of the T -algebra for the association scheme Kn1&m22;Kn2&m22;&cdots; &m22;KnD . We also show that the wreath power Km&m22;D =Km&m22;Km&m22;&cdots;&m22;Km , D copies of Km, is formally self-dual. We give a complete description of the irreducible T -modules and the structure of T -algebra for Km&m22;D for m ≥ 2 by essentially studying the irreducible modules of 2 copies of Km and then extending it to the general case for D copies of Km. Through these calculations we obtain that the T -algebra for Km&m22;D is MD+1C ⊕C⊕12 DD+1 for m ≥ 3, and MD+1C ⊕C⊕12 DD-1 m = 2.

DOI

https://doi.org/10.31274/rtd-180813-16891

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Gargi Bhattacharyya

Language

en

Proquest ID

AAI3316196

OCLC Number

271244700

ISBN

9780549688303

File Format

application/pdf

File Size

84 pages

Included in

Mathematics Commons

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