Algebraic Combinatorics Seminar - Hugh Thomas

Title: Reverse plane partitions via quiver representations

Abstract:

Let $\lambda$ be a partition. The reverse plane partitions of shape $\lambda$ are a kind of filling of the Ferrers diagram of $\lambda$ by non-negative integers. Richard Stanley found the generating function which enumerates them according to the sum of the entries. This series suggests that reverse plane partitions should be thought of as being built out of elementary building blocks corresponding to the boxes of $\lambda$. This then leads to the question of how to divide a reverse plane partition up into its component pieces. The first way to do this was found by Hillman and Grassl, thereby giving a​​​​​​​ bijective proof of Stanley's result. I will present a simple way to accomplish the same thing which goes via quiver representations. (The simplicity is due to letting representation theory take care of the​​​​​​​ combinatorics for us.) No prior knowledge of quiver representations will be assumed. This talk is based on joint work with Al Garver and Becky Patrias, arXiv:1812.08345.