UBC Discrete Math Seminar: Ethan Shelburne

We introduce a combinatorial object corresponding to a graph G, called a special rim hook G-tabloid. We construct sign-reversing maps on these special rim hook G-tabloids to prove that a family of claw-free graphs called generalized nets are Schur-positive. Thus, we make progress toward the famous conjecture of Stanley that all claw-free graphs are Schur-positive. We also discuss how this method can be extended and applied to related families of graphs.