Edge Ideals via Independence Polynomials of Graphs — Dalena Vien (Bryn Mawr)

Abstract: Edge ideals of graphs provide a fertile ground for uncovering combinatorial expressions for algebraic invariants of squarefree monomial ideals. Many algebraic invariants of these edge ideals directly reflect combinatorial properties of their underlying graphs. In this talk, I will discuss how the independence polynomial \(P_G(x)\), the generating function for independent sets of a graph \(G\), encodes surprisingly rich information about the Hilbert series of the corresponding edge ideal \(I(G)\). In particular, I will explain how \(P_G(x)\) determines both the top coefficient and degree of the \(h\)-polynomial. I will then demonstrate the results through familiar examples and a simple suspension construction that lets us track these invariants cleanly.

For questions about the event, please contact your CCMS Colloquium chairs:

Prof. Robert Cass (Robert.Cass@ClaremontMcKenna.edu) or Prof. Qidi Peng (Qidi.Peng@cgu.edu)

For logistical questions, contact Maxwell Kooiker (Maxwell.Kooiker@cgu.edu), the CCMS Colloquium Assistant.