The Chain Polynomials of Noncrossing Partition Lattices are Real-Rooted

Explore a 19-minute mathematics lecture from the Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability" at the Erwin Schrödinger International Institute that delves into the real-rootedness of chain polynomials in noncrossing partition lattices. Learn about the coefficients of chain polynomials in finite posets and their role in enumerating chains by element count. Discover proven results about noncrossing partition lattices associated with finite Coxeter groups and examine formulas for h-polynomials in irreducible cases, presented as collaborative research with Christos Athanasiadis and Theo Douvropoulos.