Symmetric structures in the weak and strong Bruhat orders
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 hu...
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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/1721.1/145042 |
| Summary: | 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. |
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