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Higher Weak Order of Affine Permutations

Herman Chau, University of Washington
Wednesday, March 8, 2023 - 4:00pm to 5:30pm
PDL C-401 and via Zoom Link:
Herman Chau
Herman Chau


We generalize the higher weak orders of Manin and Schechtmann to arbitrary permutations \$w\$ in the affine symmetric group \$\widetilde{S}_n\$. We show that the 2nd higher weak order \$B_{n,2}(w)\$ is a bounded graded poset with unique minimal and maximal elements and conjecture based on partial results and computational evidence, that the same is true for all \$B_{n,k}(w)\$ where \$2 \le k \le n\$. We also prove an upper bound on \$|B_{n,2}(w)|\$ via a combinatorial structure we call a weaving pattern. This is joint work with Sara Billey, Ben Elias, and Kevin Liu.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 4:00–4:30. The main talk starts at 4:40.

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Meeting ID: 915 4733 5974