Foster Tom

We prove a new signed elementary symmetric function expansion of the chromatic symmetric function. We then use sign-reversing involutions to prove e -positivity for graphs formed by joining cycles or cliques at single vertices. By considering...

We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use sign-reversing involutions to prove new combinatorial formulas for melting lollipops and for K...

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...

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...