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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University of Waterloo
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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 |
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en |
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Mathematics partition genus permutation hypermonopole generating series poset rank-symmetric symmetric chain order |
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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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1716572892318138368 |