Discrete Math Seminar: Foster Tom

Schur functions form the most interesting and important basis for the algebra of symmetric functions. They have connections to representation theory and algebraic geometry, and satisfy a multitude of beautiful combinatorial identities. We investigate an algebraic relationship between ribbon Schur functions, a generalization of Schur functions. More specifically, we consider when the difference between two ribbon Schur functions is a single Schur function. We will see that this near-equality phenomenon occurs for fourteen infinite families and we will present conditions under which these are the only possibilities.