A universal approach to quasisymmetric generating functionsMarcelo AguiarCRMISM, Université de Montréal
May 4,

ABSTRACT


We will discuss a universal procedure for the construction and study of several generating functions arising in combinatorics, within the framework of Hopf algebras. For several types of combinatorial objects, a natural Hopf algebra will be defined, and a "zeta" functional on it. To these, one associates a "Mobius" functional, a "zeta" polynomial and a "flag" quasisymmetric function, by means of a universal property. The terminology is taken from the case of posets. The basic facts and relationships between these objects hold in general. Instances of the zeta polynomial are:
Instances of the flag quasisymmetric function are:

Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

