Yifeng Huang

Partitions arise in linear algebra as Smith normal forms of finite DVR-modules. This viewpoint has given rise to several important objects in symmetric function theory; they are indexed by partitions. What if we replace the DVR by other rings? The...

In 1958, Fine and Herstein proved that the an n by n matrix over the finite field F_q has a probability of q^{-n} to be nilpotent. A clever application of this result can lead to the formula \sum_{H: abelian p-group} 1/|Aut(H)| = 1/((1-p^-1)(1-p^-2)...