Date: Friday, September 06, 2019
Location: 4096 East Hall (3:00 PM to 4:00 PM)
Title: Cycle index and CohenLenstra distributions given by padic matrices
Abstract: Classically, the cycle index of a permutation group is a polynomial developed to count colorings modulo an action of the group, often known as the PĆ³lya enumeration theorem. The generating function whose nth coefficient is given by the cycle index of the full symmetric group of n letters has an interesting factorization property. In this talk, we will dive into the structure behind this factorization, which is also present for n x n matrices over the finite field of p elements. As an application, we will generalize two results of Friedman and Washington on the asymptotic distribution of the cokernal of a random n x n integral padic matrix with respect to the Haar measure, when n goes to infinity. The limiting distribution follows a generalized version of the CohenLenstra distribution.
This is joint work with Yifeng Huang.
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Speaker: Gilyoung Cheong
Institution: University of Michigan
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