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Hyperpfaffians in Algebraic Combinatorics

dc.contributor.authorRedelmeier, Danielen
dc.date.accessioned2006-08-22T14:28:24Z
dc.date.available2006-08-22T14:28:24Z
dc.date.issued2006en
dc.date.submitted2006en
dc.description.abstractThe pfaffian is a classical tool which can be regarded as a generalization of the determinant. The hyperpfaffian, which was introduced by Barvinok, generalizes the pfaffian to higher dimension. This was further developed by Luque, Thibon and Abdesselam. There are several non-equivalent definitions for the hyperpfaffian, which are discussed in the introduction of this thesis. Following this we examine the extension of the Matrix-Tree theorem to the Hyperpfaffian-Cactus theorem by Abdesselam, proving it without the use of the Grassman-Berezin Calculus and with the new terminology of the non-uniform hyperpfaffian. Next we look at the extension of pfaffian orientations for counting matchings on graphs to hyperpfaffian orientations for counting matchings on hypergraphs. Finally pfaffian rings and ideal s are extended to hyperpfaffian rings and ideals, but we show that under reason able assumptions the algebra with straightening law structure of these rings cannot be extended.en
dc.formatapplication/pdfen
dc.format.extent709478 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10012/1055
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2006, Redelmeier, Daniel. All rights reserved.en
dc.subjectMathematicsen
dc.subjectHyperpfaffianen
dc.subjectPfaffianen
dc.subjectCombinatoricsen
dc.titleHyperpfaffians in Algebraic Combinatoricsen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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