The MalvenutoReutenauer Hopf Algebra of PermutationsFrank SottileUniversity of Massachusetts, Amherst
October 24,

ABSTRACT


Gessel's enumerator of posets partitions may be seen as a morphism from a Hopf algebra of labeled posets to the Hopf algebra of quasisymmetric functions. This map factors through a third Hopf algebra consisting of permutations, which was introduced by Malvenuto and Reutenauer. This talk will describe the structure of this MalvenutoReutenauer Hopf algebra in detailed combinatorial terms. This description is obtained through careful analysis of the weak Bruhat order on the symmetric groups and their subsets of shuffles. This is joint work with Marcelo Aguiar. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

