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Noncommutative Schur P-functions and the Shifted Plactic Monoid.

dc.contributor.authorSerrano Herrera, Luis Guillermoen_US
dc.date.accessioned2010-08-27T15:19:48Z
dc.date.availableNO_RESTRICTIONen_US
dc.date.available2010-08-27T15:19:48Z
dc.date.issued2010en_US
dc.date.submitteden_US
dc.identifier.urihttps://hdl.handle.net/2027.42/77864
dc.description.abstractThis thesis is comprised of two related projects involving shifted tableaux. In the first project, we introduce a shifted analog of the plactic monoid of Lascoux and Schutzenberger, the shifted plactic monoid. It can be defined in two different ways: via the shifted Knuth relations, or using Haiman's mixed insertion. Applications of the theory of the shifted plactic monoid include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion of a Schur P-function; a shifted counterpart of the Lascoux-Schutzenberger theory of noncommutative Schur functions in plactic variables; a characterization of shifted tableau words; and more. In the second project, joint with T. K. Petersen, we show that the set of reduced expressions for the longest element in the hyperoctahedral group exhibits the cyclic sieving phenomenon. The proofs rely heavily on the theory of the shifted plactic monoid.en_US
dc.format.extent407868 bytes
dc.format.extent1373 bytes
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dc.language.isoen_USen_US
dc.subjectCombinatoricsen_US
dc.titleNoncommutative Schur P-functions and the Shifted Plactic Monoid.en_US
dc.typeThesisen_US
dc.description.thesisdegreenamePh.D.en_US
dc.description.thesisdegreedisciplineMathematicsen_US
dc.description.thesisdegreegrantorUniversity of Michigan, Horace H. Rackham School of Graduate Studiesen_US
dc.contributor.committeememberFomin, Sergeyen_US
dc.contributor.committeememberLam, Thomasen_US
dc.contributor.committeememberPalomino, Franciso Joseen_US
dc.contributor.committeememberStembridge, John R.en_US
dc.contributor.committeememberUribe-Ahumada, Alejandroen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/77864/1/lserrano_1.pdf
dc.owningcollnameDissertations and Theses (Ph.D. and Master's)


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