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dc.contributor.authorClokie, Trevor
dc.date.accessioned2021-02-02 15:45:13 (GMT)
dc.date.available2021-02-02 15:45:13 (GMT)
dc.date.issued2021-02-02
dc.date.submitted2021-01-29
dc.identifier.urihttp://hdl.handle.net/10012/16786
dc.description.abstractLet s_2(n) be the sum of the digits of n when expressed in base 2. For integers n and k, Stolarsky defined n to be k-flimsy if s_2(kn) < s_2(n). In this paper, we generalize the definition of k-flimsy numbers to all bases b, and provide a method to construct a pushdown automaton recognizing the k-flimsy base-b numbers. Using the tools of context-free languages and analytic combinatorics, we use this automaton to determine precise asymptotics for the number of k-flimsy N-digit numbers in base b. Lastly, using the results we obtained, we discuss the natural densities of k-flimsy numbers in base b for all values k and b. Our main results can be found in Theorems 2, 3, 8, and 9.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectpushdown automatonen
dc.subjectcontext-free languageen
dc.subjectflimsy numberen
dc.titleCounting Flimsy Numbers via Formal Language Theoryen
dc.typeMaster Thesisen
dc.pendingfalse
uws-etd.degree.departmentDavid R. Cheriton School of Computer Scienceen
uws-etd.degree.disciplineComputer Scienceen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws-etd.embargo.terms0en
uws.contributor.advisorShallit, Jeffrey
uws.contributor.affiliation1Faculty of Mathematicsen
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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