Differential posets and dual graded graphs
Thesis (S. M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2009
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| Online Access: | http://hdl.handle.net/1721.1/47899 |
| _version_ | 1826210023201570816 |
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| author | Qing, Yulan, S.M. Massachusetts Institute of Technology |
| author2 | Richard Stanley. |
| author_facet | Richard Stanley. Qing, Yulan, S.M. Massachusetts Institute of Technology |
| author_sort | Qing, Yulan, S.M. Massachusetts Institute of Technology |
| collection | MIT |
| description | Thesis (S. M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. |
| first_indexed | 2024-09-23T14:40:01Z |
| format | Thesis |
| id | mit-1721.1/47899 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:40:01Z |
| publishDate | 2009 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/478992019-04-12T15:47:10Z Differential posets and dual graded graphs Qing, Yulan, S.M. Massachusetts Institute of Technology Richard Stanley. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (S. M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. Includes bibliographical references (leaf 53). In this thesis I study r-differential posets and dual graded graphs. Differential posets are partially ordered sets whose elements form the basis of a vector space that satisfies DU-UD=rI, where U and D are certain order-raising and order-lowering operators. New results are presented related to the growth and classification of differential posets. In particular, we prove that the rank sequence of an r-differential poset is bounded above by the Fibonacci sequence and that there is a unique poset with such a maximum rank sequence. We also prove that a 1-differential lattice is either Young's lattice or the Fibonacci lattice. In the second part of the thesis, we present a series of new examples of dual graded graphs that are not isomorphic to the ones presented in Fomin's original paper. by Yulan Qing. S.M. 2009-10-01T16:00:57Z 2009-10-01T16:00:57Z 2008 2008 Thesis http://hdl.handle.net/1721.1/47899 436221569 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 53 leaves application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Qing, Yulan, S.M. Massachusetts Institute of Technology Differential posets and dual graded graphs |
| title | Differential posets and dual graded graphs |
| title_full | Differential posets and dual graded graphs |
| title_fullStr | Differential posets and dual graded graphs |
| title_full_unstemmed | Differential posets and dual graded graphs |
| title_short | Differential posets and dual graded graphs |
| title_sort | differential posets and dual graded graphs |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/47899 |
| work_keys_str_mv | AT qingyulansmmassachusettsinstituteoftechnology differentialposetsanddualgradedgraphs |