Discrete Math Seminar: Andrew Berget

A length $n$ parking function is a sequence of integers whose non-decreasing rearrangement $(q_1,q_2,\dots,q_n)$ satisfies $q_i \leq i$. Any rearrangement of a parking function thus remains a parking function and one can consider the permutation representation $P_n$ of the symmetric groups $S_n$ generated by such sequences. In this talk I will describe a representation of $S_{n+1}$ whose restriction to $S_n$ is $P_n$. This will be viewed in the context of a result of Stanley which extends the regular representation of $S_n$ to a representation of $S_{n+1}$. I'll include a review of the combinatorics of symmetric group representations. This is joint work with Brendon Rhoades.