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dc.contributor.advisorOh, Suho
dc.contributor.authorMcAlmon, Robert ( Orcid Icon 0000-0003-2547-9612 )
dc.date.accessioned2018-08-03T19:14:52Z
dc.date.available2018-08-03T19:14:52Z
dc.date.issued2018-07-20
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/7366
dc.description.abstractIn the paper “Bruhat order, rationally smooth Schubert varieties, and hyperplane arrangements,” S. Oh and H. Yoo studied Schubert varieties in generalized flag manifolds by linking them with a certain hyperplane arrangement coming from the reflection synmmetries of a Weyl group. They made two conjectures. The first relates to a curious property of maximal parabolic quotients of finite Weyl groups. The second states that for an element w of a finite Coxeter group W, the generating function R_w(q) of its hyperplane arrangement coincides with the rank-generating function P_w(q) of its lower interval [e,w] in the Bruhat order, if and only if [e, w] is rank-symmetric. Here, we generalize the first conjecture for finite Coxeter groups and prove it. We use this result to prove the second conjecture. Two chapters of background material on Coxeter systems and hyperplane arangements are provided.
dc.formatText
dc.format.extent48 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_US
dc.subjectBruhat order
dc.subjectParabolic quotients
dc.subjectHyperplanes
dc.subjectCoxeter arrangement
dc.subjectPalindromic
dc.subject.lcshSymmetric functionsen_US
dc.subject.lcshSchubert varietiesen_US
dc.titleBruhat Order and Coxeter Hyperplane Arrangements
txstate.documenttypeThesis
dc.contributor.committeeMemberCurtin, Eugene
dc.contributor.committeeMemberKeller, Thomas
dc.contributor.committeeMemberRusnak, Lucas
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas State University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science
txstate.departmentMathematics


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