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Sunday, October 25, 2020

**Abstract:** It is a classical result that any permutation in the symmetric group can be generated by a sequence of adjacent transpositions. The sequences of minimal length are called reduced words. The graphs of these reduced words, with edges determined by relations in the underlying Coxeter group, have been well studied. Recently, the diameter has been calculated for the longest permutation $n\ldots 21$ by Reiner and Roichman as well as Assaf. In this talk we present our results on diameters for certain classes or permutations. We also make progress on conjectured bounds of the diameter by Reiner and Roichman, which are based on the underlying hyperplane arrangement. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Monday, October 26, 2020

Tuesday, October 27, 2020

Wednesday, October 28, 2020

Thursday, October 29, 2020

Friday, October 30, 2020