New combinatorics of the weak and strong Bruhat orders
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology