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 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.

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

2021

Author dc:creator

• Gaetz, Christian

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/1721.1/139101

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/139101