The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. It has been a challenging open problem to determine which posets have real-rooted chain polynomials. In this talk we prove that noncrossing partition lattices associated to finite Coxeter groups have that property. We also present formulas for the h-polynomials of theses posets, for the irreducible cases.
This is joint work with Christos Athanasiadis and Theo Douvropoulos.