Dissertation/Thesis Abstract

Nets and translation nets of higher dimensions
by Swaminathan, Ganesh, Ph.D., National University of Singapore (Singapore), 2015, 89; 10006001
Abstract (Summary)

Finite Geometry has been one of the interesting areas of research in the field of Combinatorics and has seen tremendous advancement in the 20th century after the introduction of Finite Nets by R. H. Bruck in 1951. In the early chapters of the thesis, we survey the concept of “Nets (finite) and Translation Nets” in two dimension and in three dimension. We also try to fill in the gaps found and formulate equivalent mathematical definitions. Some of the drawbacks in Laskar’s definition for nets of dimension three led to the redefinition by fixing the parameters involved. Then, the concept of “partial congruence partition” in three dimension, denoted by PCP(3), is introduced and the equivalence of PCP(3) and translation nets of dimension three is also proved. The latter chapters cover the concept of Association Scheme and extend the definition of a net and partial congruence partition to n-dimension. Several new parameters for “Association Scheme of class 3” are also derived. (Abstract shortened by UMI.)

Indexing (document details)
School: National University of Singapore (Singapore)
Department: Mathematics
School Location: Republic of Singapore
Source: DAI-B 77/06(E), Dissertation Abstracts International
Subjects: Mathematics
Publication Number: 10006001
ISBN: 978-1-339-43870-2
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