Abstract:
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