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dc.contributor.advisorRichard P. Stanley.en_US
dc.contributor.authorTenner, Bridget Eileenen_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2006-11-07T13:36:48Z
dc.date.available2006-11-07T13:36:48Z
dc.date.copyright2006en_US
dc.date.issued2006en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/34617
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.en_US
dc.descriptionIncludes bibliographical references (p. 85-88) and index.en_US
dc.description.abstractThis thesis examines several aspects of reduced decompositions in finite Coxeter groups. Effort is primarily concentrated on the symmetric group, although some discussions are subsequently expanded to finite Coxeter groups of types B and D. In the symmetric group, the combined frameworks of permutation patterns and reduced decompositions are used to prove a new characterization of vexillary permutations. This characterization and the methods used yield a variety of new results about the structure of several objects relating to a permutation. These include its commutation classes, the corresponding graph of the classes, the zonotopal tilings of a particular polygon, and a poset defined in terms of these tilings. The class of freely braided permutations behaves particularly well, and its graphs and posets are explicitly determined. The Bruhat order for the symmetric group is examined, and the permutations with boolean principal order ideals are completely characterized. These form an order ideal which is a simplicial poset, and its rank generating function is computed. Moreover, it is determined when the set of permutations avoiding a particular set of patterns is an order ideal, and the rank generating functions of these ideals are computed.en_US
dc.description.abstract(cont.) The structure of the intervals and order ideals in this poset is elucidated via patterns, including progress towards understanding the relationship between pattern containment and subintervals in principal order ideals. The final discussions of the thesis are on reduced decompositions in the finite Coxeter groups of types B and D. Reduced decompositions of the longest element in the hyperoctahedral group are studied, and expected values are calculated, expanding on previous work for the symmetric group. These expected values give a quantitative interpretation of the effects of the Coxeter relations on reduced decompositions of the longest element in this group. Finally, the Bruhat order in types B and D is studied, and the elements in these groups with boolean principal order ideals are characterized and enumerated by length.en_US
dc.description.statementofresponsibilityby Bridget Eileen Tenner.en_US
dc.format.extent90en_US
dc.format.extent4962834 bytes
dc.format.extent4966523 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectMathematics.en_US
dc.titleThe combinatorics of reduced decompositionsen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.identifier.oclc71331121en_US


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