Posets and Hopf AlgebrasMike ZabrockiYork University
October 24,

ABSTRACT


Within the last few years there has been an interest in the literature on spaces which generalize and are analogous to the algebra of symmetric functions. We will give a survey that will be of interest to a general audience of some of these spaces: the noncommmutative symmetric functions of Gelfand/Krob/Lascoux/Leclerc/Retakh/Thibon/et al., the noncommutative symmetric functions of Rosas/Sagan, the quasisymmetric functions of Gessel, the MalvenutoReutenauer algebra of permutations and a new space which we call the noncommutative quasisymmetric functions. The purpose of this talk will be to show how these spaces relate to each other and to describe how posets on the indexing set are used to define bases of these spaces with interesting algebraic properties. This is joint work with Nantel Bergeron 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

