New and existing results on circular words

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dc.contributor.authorJohnson, Jesse T.
dc.contributor.supervisorCurrie, James
dc.contributor.supervisorMacGillivray, Gary
dc.date.accessioned2020-05-09T03:27:02Z
dc.date.available2020-05-09T03:27:02Z
dc.date.copyright2020en_US
dc.date.issued2020-05-08
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractCircular words, also known as necklaces, are combinatorial objects closely related to linear words. A brief history of circular words is given, from their early conception to present results. We introduce the concept of a level word, that being a word containing a equal or roughly equal amount of each letter. We characterize exactly the lengths for which level square free circular words on three letters exist. This is accomplished through a modification of Shur’s construction of square-free circular words. A word on two letters is called a Frankel-Simpson word if the only squares it contains are 00, 11, and 0101. Using the result mentioned above and several computer searches, we characterize exactly the lengths for which circular Frankel-Simpson words exist, and give an example or construction for each.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/11743
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectCircular wordsen_US
dc.subjectFrankel-Simpsonen_US
dc.subjectSquare-free wordsen_US
dc.subjectnecklacesen_US
dc.titleNew and existing results on circular wordsen_US
dc.typeThesisen_US

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