New combinatorics of the weak and strong Bruhat orders
This thesis describes a line of work, much of it joint with Yibo Gao, which began with our proof of Stanley's conjecture that the weak order on the symmetric group is Sperner. Further developments---either directly related or related in our thinking at the time---involve weighted path enumerat...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2022
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| Online Access: | https://hdl.handle.net/1721.1/139101 |
| _version_ | 1826211117360218112 |
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| author | Gaetz, Christian |
| author2 | Postnikov, Alexander |
| author_facet | Postnikov, Alexander Gaetz, Christian |
| author_sort | Gaetz, Christian |
| collection | MIT |
| description | This thesis describes a line of work, much of it joint with Yibo Gao, which began with our proof of Stanley's conjecture that the weak order on the symmetric group is Sperner. Further developments---either directly related or related in our thinking at the time---involve weighted path enumeration in the weak and strong Bruhat orders, specializations of Schubert polynomials, separable elements in finite Weyl groups, and inequalities for linear extensions of finite posets. |
| first_indexed | 2024-09-23T15:00:52Z |
| format | Thesis |
| id | mit-1721.1/139101 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T15:00:52Z |
| publishDate | 2022 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1391012022-01-15T03:13:24Z New combinatorics of the weak and strong Bruhat orders Gaetz, Christian Postnikov, Alexander Massachusetts Institute of Technology. Department of Mathematics This thesis describes a line of work, much of it joint with Yibo Gao, which began with our proof of Stanley's conjecture that the weak order on the symmetric group is Sperner. Further developments---either directly related or related in our thinking at the time---involve weighted path enumeration in the weak and strong Bruhat orders, specializations of Schubert polynomials, separable elements in finite Weyl groups, and inequalities for linear extensions of finite posets. Ph.D. 2022-01-14T14:49:55Z 2022-01-14T14:49:55Z 2021-06 2021-05-25T12:46:57.096Z Thesis https://hdl.handle.net/1721.1/139101 0000-0002-3748-4008 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Gaetz, Christian New combinatorics of the weak and strong Bruhat orders |
| title | New combinatorics of the weak and strong Bruhat orders |
| title_full | New combinatorics of the weak and strong Bruhat orders |
| title_fullStr | New combinatorics of the weak and strong Bruhat orders |
| title_full_unstemmed | New combinatorics of the weak and strong Bruhat orders |
| title_short | New combinatorics of the weak and strong Bruhat orders |
| title_sort | new combinatorics of the weak and strong bruhat orders |
| url | https://hdl.handle.net/1721.1/139101 |
| work_keys_str_mv | AT gaetzchristian newcombinatoricsoftheweakandstrongbruhatorders |