New combinatorics of the weak and strong Bruhat orders
Name
gaetz-gaetz-phd-math-2021-thesis.pdf
Description
Thesis PDF
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697.26 KB
Format
Adobe PDF
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53db12d37a361233fe7d2b7c0faa253c
Author(s)
Gaetz, Christian
Advisor(s)
Postnikov, Alexander
Date Issued
June 2021
Publisher
Massachusetts Institute of Technology
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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