Selected topics in addition chains

dc.creatorGiese, Robert Paul
dc.date.accessioned2022-06-20T20:30:28Z
dc.date.available2022-06-20T20:30:28Z
dc.date.copyright1974
dc.date.issued1974
dc.description.abstractW. R. Utz conjectured that [lowercase l](2n) = [lowercase l](n) + 1. D. Knuth found four counterexamples to Utz's conjecture. He then modified it to [lowercase l](2n) > [lowercase l](n) and more generally [lowercase l](mn) > [lowercase l](n). This dissertation contains an infinite number of counterexamples to Knuth's modification of the Utz conjecture. A conjecture is proposed by this author that has the theorems of Utz, Subbarao, and Knuth concerning addition chains as corollaries: If [lowercase l](n) = [lambda](n) + k, then [nu](n) < 2[raised k]. Knuth introduced a sequence c, exhibited the first few terms of the sequence, and proposed an asymptotic limit theorem. In this paper an asymptotic limit theorem is proven for c: If lim (c(r))/([Phi][raised r]) = 1, then [Phi] = 2.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other13695504
dc.identifier.urihttps://hdl.handle.net/10657/9521
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleSelected topics in addition chains
dc.type.dcmiText
dc.type.genreThesis
dcterms.accessRightsThe full text of this item is not available at this time because it contains documents that are presumed to be under copyright and are accessible only to users who have an active CougarNet ID. This item will continue to be made available through interlibrary loan.
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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