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A Novel Insertion Algorithm

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dc.contributor.authorQuinlan, Isisen
dc.contributor.committeechairShimozono, Mark M.en
dc.contributor.committeememberOrr, Daniel D.en
dc.contributor.committeememberLoehr, Nicholas A.en
dc.contributor.committeememberMihalcea, Constantin Leonardoen
dc.contributor.departmentMathematicsen
dc.date.accessioned2024-05-10T08:00:15Zen
dc.date.available2024-05-10T08:00:15Zen
dc.date.issued2024-05-09en
dc.description.abstractThrough the definition of a new insertion algorithm this paper seeks to provide an alternative to the existing bijections between permutations and certain kinds of tableaux. We will define two versions of each algorithm covered, both the existing ones and the novel one. These different constructions will include one using a lot of small intermediate steps and one which directly creates the tableaux from the permutation. After showing that these are equivalent, we will briefly discuss the results of pattern avoidance on tableau shape.en
dc.description.abstractgeneralBuilding up tableaux from permutations can be a helpful way to get information about that permutation without having to check by hand. Different methods of building tableaux will tell us different types of information about the permutation. For that reason, we are defining a new method of building tableaux so that we can extract useful information from the permutations used.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:40607en
dc.identifier.urihttps://hdl.handle.net/10919/118942en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectalgebraic combinatoricsen
dc.titleA Novel Insertion Algorithmen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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