Discrete Applied Math Seminar by Foster Tom: A Signed E-expansion of the Chromatic Symmetric Function and Some New E-positive Graphs
Foster Tom, postdoctoral instructor, Massachusetts Institute of Technology
A Signed E-expansion of the Chromatic Symmetric Function and Some New E-positive Graphs
We prove a new signed elementary symmetric function expansion of the chromatic symmetric function of any unit interval graph. We then use sign-reversing involutions to prove new combinatorial formulas for many families of graphs, including the K-chains studied by Gebhard and Sagan, formed by joining cliques at single vertices, and for graphs obtained from them by removing any number of edges from any of the cut vertices. We also introduce a version for the quasisymmetric refinement of Shareshian and Wachs.
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