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dc.contributor.authorYip, Marthaen
dc.date.accessioned2007-05-08 14:01:22 (GMT)
dc.date.available2007-05-08 14:01:22 (GMT)
dc.date.issued2006en
dc.date.submitted2006en
dc.identifier.urihttp://hdl.handle.net/10012/2933
dc.description.abstractWe obtain a tight upper bound for the genus of a partition, and calculate the number of partitions of maximal genus. The generating series for genus zero and genus one rooted hypermonopoles is obtained in closed form by specializing the genus series for hypermaps. We discuss the connection between partitions and rooted hypermonopoles, and suggest how a generating series for genus one partitions may be obtained via the generating series for genus one rooted hypermonopoles. An involution on the poset of genus one partitions is constructed from the associated hypermonopole diagrams, showing that the poset is rank-symmetric. Also, a symmetric chain decomposition is constructed for the poset of genus one partitions, which consequently shows that it is strongly Sperner.en
dc.formatapplication/pdfen
dc.format.extent608255 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2006, Yip, Martha. All rights reserved.en
dc.subjectMathematicsen
dc.subjectpartitionen
dc.subjectgenusen
dc.subjectpermutationen
dc.subjecthypermonopoleen
dc.subjectgenerating seriesen
dc.subjectposeten
dc.subjectrank-symmetricen
dc.subjectsymmetric chain orderen
dc.titleGenus one partitionsen
dc.typeMaster Thesisen
dc.pendingfalseen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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