Abstract:
For each permutation \$w\$, we consider the set \$\mathrm{PD}(w)\$ of reduced pipe dreams for \$w\$, partially ordered so that cover relations correspond to (generalized) chute moves. Settling a conjecture of Rubey from 2012, we prove that \$\mathrm{PD}(w)\$ is a lattice. To establish this result, we provide a global description of the partial order on \$\mathrm{PD}(w)\$ by showing that \$\mathrm{PD}(w)\$ is isomorphic to a poset consisting of objects called Lehmer tableaux. In addition, we prove that \$\mathrm{PD}(w)\$ is a semidistributive polygonal lattice whose polygons are all diamonds or pentagons.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974