Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/121927
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dc.titleNETS AND TRANSLATION NETS OF HIGHER DIMENSIONS
dc.contributor.authorGANESH SWAMINATHAN
dc.date.accessioned2015-12-31T18:00:30Z
dc.date.available2015-12-31T18:00:30Z
dc.date.issued2015-06-15
dc.identifier.citationGANESH SWAMINATHAN (2015-06-15). NETS AND TRANSLATION NETS OF HIGHER DIMENSIONS. ScholarBank@NUS Repository.
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/121927
dc.description.abstractThesis starts with the introduction to ?Nets (finite)? in two dimension (2- nets) as given by Bruck and then proceed to three dimension (3-nets), which is due to Laskar. We also address the issues found in the basic properties of 2-nets and 3-nets by listing out the resolutions. Some of the drawbacks in Laskar?s definition for nets of dimension three led to the redefinition of 3-nets by fixing the parameters involved. We also prove that Laskar?s definition can be recovered from our new definition (except for a particular case). Translation Nets and partial congruence partition (PCP) are then surveyed in two dimension. Later, we introduce the concept of ?PCP? in three dimension denoted by PCP^(3) and prove the equivalence of PCP^(3) and translation nets of dimension three. We conclude with the definitions of Nets and PCP in n-dimension. Examples and properties are also stated.
dc.language.isoen
dc.subjectNets, MOLS and Nets, Translation nets, Partial congruence partition, Association Scheme, Higher dimensional nets
dc.typeThesis
dc.contributor.departmentMATHEMATICS
dc.contributor.supervisorMA SIU LUN, LEO
dc.description.degreeMaster's
dc.description.degreeconferredMASTER OF SCIENCE
dc.identifier.isiutNOT_IN_WOS
Appears in Collections:Master's Theses (Open)

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