Discrete Math Seminar: Foster Tom

Schur functions form an important basis for the space of symmetric functions and show up in areas from representation theory to quantum mechanics. Given an appropriate diagram of boxes, we construct its corresponding Schur function by counting the numbers of tableaux: fillings of these boxes with positive integers that satisfy some simple conditions. We then form the Schur-positivity partially ordered set by comparing these numbers of tableaux. In this talk, we present some new results of how order relations in this partially ordered set can be derived from properties of the diagrams. We then present some progress toward long-standing conjectures.