{TALK
{"October 24}
{"The Malvenuto-Reutenauer Hopf Algebra of Permutations}
{"Frank Sottile}
{"University of Massachusetts, Amherst}
{"sottile@math.umass.edu}
{"
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 Malvenuto-Reutenauer
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.