Sums of subsets of certain algebraic systems Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/1z40kz14f

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  • In this thesis we investigate the extension of certain theorems of additive number theory to three algebraic systems. A generalization of a theorem by Cauchy and Davenport on the cardinality of the sum of two sets of residue classes is given. We obtain and compare estimates for the order of a basis set of n-dimensional lattice points. These estimates are obtained using the best density inequality theorems available for the densities of Schnirelmann, Kasch and Kvarda. Finally additive number theory is extended to Boolean algebra. First, cardinality conditions are found for a given element to be in a sum (product) of sets. Next, the cardinality of the sum (product) of two sets is investigated. Finally, a modified sum is studied and some conjectures are made.
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  • File scanned at 300 ppi (Monochrome) using ScandAll PRO 1.8.1 on a Fi-6670 in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2010-08-12T17:32:34Z (GMT) No. of bitstreams: 1 HigdemRogerLeon1971.pdf: 659015 bytes, checksum: b6b88a618ec200ce3fe3cb2507a276e3 (MD5)
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2010-08-12T17:30:07Z (GMT) No. of bitstreams: 1 HigdemRogerLeon1971.pdf: 659015 bytes, checksum: b6b88a618ec200ce3fe3cb2507a276e3 (MD5)
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