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Colorful Permutation Statistics and Cycle Type

Kevin Liu, University of Washington
Wednesday, May 22, 2024 - 3:30pm to 5:00pm
PDL C-401 and via Zoom Link:
Kevin Liu
Kevin Liu


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:
Meeting ID: 915 4733 5974