A Cornucopia Of Labeled Diagrams And Their Generating Polynomials

dc.contributor.advisorJames Haglund
dc.contributor.authorWang, George
dc.date2023-05-18T01:15:02.000
dc.date.accessioned2023-05-22T18:02:39Z
dc.date.available2001-01-01T00:00:00Z
dc.date.copyright2021-08-31T20:21:00-07:00
dc.date.issued2021-01-01
dc.date.submitted2021-08-31T03:50:43-07:00
dc.description.abstractCombinatorics on tableaux-like objects and understanding the relationships of various polynomial bases with each other are classical explorations in algebraic combinatorics. This type of exploration is the focus of this dissertation. In the world of symmetric polynomials and their corresponding objects, we prove some partial results for the Schur expansion of Jack polynomials in certain binomial coefficient bases. As a result, we conjecture a bijection between tableaux and rook boards, which spurs some further exploration of quasi-Yamanouchi tableaux as combinatorial objects of their own merit. We then move to the general polynomial ring and two of its bases, key and lock polynomials. These are each generating polynomials of certain kinds of Kohnert diagrams, and we use this connection to say something about their relationship. Each of the objects that they are generating polynomials of have a nice crystal structure. We prove that the crystal structure corresponding to lock polynomials is connected and can be embedded into the crystal structure corresponding to key polynomials.
dc.description.degreeDoctor of Philosophy (PhD)
dc.format.extent96 p.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/31185
dc.languageen
dc.legacy.articleid5884
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=5884&context=edissertations&unstamped=1
dc.provenanceReceived from ProQuest
dc.rightsGeorge Wang
dc.source.issue4098
dc.source.journalPublicly Accessible Penn Dissertations
dc.source.statuspublished
dc.subject.othercrystal
dc.subject.othergenerating polynomial
dc.subject.othernonsymmetric
dc.subject.othersymmetric
dc.subject.othertableaux
dc.subject.otherMathematics
dc.titleA Cornucopia Of Labeled Diagrams And Their Generating Polynomials
dc.typeDissertation/Thesis
digcom.contributor.authorWang, George
digcom.date.embargo2001-01-01T00:00:00-08:00
digcom.identifieredissertations/4098
digcom.identifier.contextkey24594906
digcom.identifier.submissionpathedissertations/4098
digcom.typedissertation
dspace.entity.typePublication
upenn.graduate.groupMathematics
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