2026-09-19T20:13:18Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1450422022-08-30T03:26:56Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Postnikov, Alexander
Gao, Yibo
Massachusetts Institute of Technology. Department of Mathematics
2022-08-29T16:29:06Z
2022-08-29T16:29:06Z
2022-05
2022-06-07T15:33:52.198Z
https://hdl.handle.net/1721.1/145042
0000-0003-3060-2259
The weak and strong Bruhat orders are classical and rich combinatorial objects, with connections to Schubert calculus, Lie algebras, hyperplane arrangements, sorting networks and so on. In this thesis, we study various new symmetries within these structures, including the balance constant and the hull metric property of the weak order, and the self-dual intervals and boolean elements in the strong order. Much of the work involved is joint with Christian Gaetz.
Ph.D.
Massachusetts Institute of Technology
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http://rightsstatements.org/page/InC-EDU/1.0/
Symmetric structures in the weak and strong Bruhat orders
Thesis
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Doctoral
Doctor of Philosophy
Publication
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