Genus one partitions

We 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 bet...

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Main Author: Yip, Martha
Format: Others
Language:en
Published: University of Waterloo 2007
Subjects:
Online Access:http://hdl.handle.net/10012/2933
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spelling ndltd-WATERLOO-oai-uwspace.uwaterloo.ca-10012-29332013-01-08T18:50:04ZYip, Martha2007-05-08T14:01:22Z2007-05-08T14:01:22Z20062006http://hdl.handle.net/10012/2933We 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.application/pdf608255 bytesapplication/pdfenUniversity of WaterlooCopyright: 2006, Yip, Martha. All rights reserved.Mathematicspartitiongenuspermutationhypermonopolegenerating seriesposetrank-symmetricsymmetric chain orderGenus one partitionsThesis or DissertationCombinatorics and OptimizationMaster of Mathematics
collection NDLTD
language en
format Others
sources NDLTD
topic Mathematics
partition
genus
permutation
hypermonopole
generating series
poset
rank-symmetric
symmetric chain order
spellingShingle Mathematics
partition
genus
permutation
hypermonopole
generating series
poset
rank-symmetric
symmetric chain order
Yip, Martha
Genus one partitions
description We 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.
author Yip, Martha
author_facet Yip, Martha
author_sort Yip, Martha
title Genus one partitions
title_short Genus one partitions
title_full Genus one partitions
title_fullStr Genus one partitions
title_full_unstemmed Genus one partitions
title_sort genus one partitions
publisher University of Waterloo
publishDate 2007
url http://hdl.handle.net/10012/2933
work_keys_str_mv AT yipmartha genusonepartitions
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