Hopf Algebras of Labeled Posets

Frank Sottile
University of Toronto

A labeled poset is a partially ordered set where each cover is labeled
with an integer.  This structure arises naturally in the theory of
shellability of posets, as well as the weak order on the symmetric
group and in the study of Schubert polynomials.

In this talk, we will introduce a generating function for
maximal chains whose sequence of edge labels have fixed descents.
The association of this generating function to such a poset
gives a Hopf algebra map from a Hopf algebra of such posets
to the algebra of quasi-symmetric functions.  We relate this
construction to the theory of symmetric functions.

No prior knowledge is assumed; definitions, constructions, and 
proofs (which are elementary) will be given.