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 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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2022

Author dc:creator

• Gao, Yibo

Advisor dc:contributor.advisor

• Postnikov, Alexander

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/145042

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/145042