|
UWSpace >
University of Waterloo >
Electronic Theses and Dissertations (UW) >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10012/2933
|
| Title: | Genus one partitions |
| Authors: | Yip, Martha |
| Keywords: | Mathematics
partition
genus
permutation
hypermonopole
generating series
poset
rank-symmetric
symmetric chain order |
| Approved Date: | 2006 |
| Date Submitted: | 2006 |
| Abstract: | 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. |
| Department: | Combinatorics and Optimization |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/2933 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
|
This item is protected by original copyright
|
All items in UWSpace are protected by copyright, with all rights reserved.
|
