Abstract:
In this talk, we consider colored permutation groups $\mathbb{Z}_m\wr S_n$, which contain the symmetric groups $S_n\cong \mathbb{Z}_1 \wr S_n$ and the signed symmetric groups $B_n\cong \mathbb{Z}_2\wr S_n$ as special cases. Like in $S_n$, colored permutations in $\mathbb{Z}_m\wr S_n$ have a notion of cycle type that classifies its conjugacy classes. We explore the distributions and moments of statistics on $\mathbb{Z}_m\wr S_n$ when refined by cycle type, with particular emphasis on the descent and flag-major index statistics when there are no "short" cycles. This talk is based on joint works with Jesse Campion Loth, Michael Levet, Sheila Sundaram, and Mei Yin.
Note (special time): This talk begins with a pre-seminar (aimed at graduate students) at 3:30–3:50. The main talk starts at 4:00.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974