Matthew Morin

We look at the problem of recovering a graph from its chromatic symmetric function. For any graph we show that some basic data can be recovered, and for special cases of trees and unicyclic graphs we can recover the graph completely.

We introduce the notion of a fat staircase and define when a skew diagram D is a sum of fat staircases. We give a collection of Schur-positivity results that may be obtained from each sum of fat staircases. Further, we determine conditions on when a...