Speaker:  Rafael González D'león, Universidad Sergio Arboleda and York University.

Title:  The Whitney dual of a graded poset

Abstract:

Two posets are Whitney duals to each other if the (absolute value of their) Whitney numbers of the first and second kind are switched between the two posets.   We introduce new types of edge and chain-edge labelings of a graded poset which we call Whitney labelings. We prove that every graded poset with a Whitney labeling has a Whitney dual and we show how to explicitly construct a Whitney dual using a technique that involves quotient posets. As an application of our main theorem, we show that geometric lattices, the lattice of noncrossing partitions, the poset of weighted partitions studied by González D'León-Wachs and the R*S-labelable posets studied by Simion-Stanley all have Whitney duals. We also show that a graded poset P with a Whitney labeling admits a local action of the 0-Hecke algebra on the set of maximal chains of P. The characteristic of the associated representation is Ehrenborg's flag quasisymmetric function of P. This is joint work with Josh Hallam (Wake Forest Universtity).

For further information, see Discrete CATS Seminar