Counting Flimsy Numbers via Formal Language Theory
| dc.contributor.author | Clokie, Trevor | |
| dc.date.accessioned | 2021-02-02T15:45:13Z | |
| dc.date.available | 2021-02-02T15:45:13Z | |
| dc.date.issued | 2021-02-02 | |
| dc.date.submitted | 2021-01-29 | |
| dc.description.abstract | Let 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.identifier.uri | http://hdl.handle.net/10012/16786 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | pushdown automaton | en |
| dc.subject | context-free language | en |
| dc.subject | flimsy number | en |
| dc.title | Counting Flimsy Numbers via Formal Language Theory | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | David R. Cheriton School of Computer Science | en |
| uws-etd.degree.discipline | Computer Science | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | Shallit, Jeffrey | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |