Discrete CATS Seminar
Master Talk
Speaker: Evan Henning, University of Kentucky
Title: The incidence Hopf algebra of the non-crossing partition lattice
Abstract:
First studied in the literature by H.W Becker as planar rhyme schemes, non-crossing partitions have long been a combinatorial object of interest. It is well known that the set of non-crossing partitions of [n] inherit a lattice structure as a sublattice of the partition lattice ordered by refinement. Simion and Ullman showed that this lattice is self-dual. Moreover, intervals in the non-crossing partition lattice factor nicely hence the incidence Hopf algebra on the family of intervals of the non-crossing partition lattice has a nice structure. In this talk we will discuss Hillary Einziger's contributions to the study of the structure of this incidence Hopf algebra. In doing so we will find multiple bases, various formulas for the antipode, and show a bijection between this Hopf algebra and that of the symmetric functions.