The Malvenuto-Reutenauer Hopf Algebra of Permutations

Frank Sottile

University of Massachusetts, Amherst

October 24,
4:15pm
refreshments at 3:45pm
2-338

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 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.

This is joint work with Marcelo Aguiar.


Speaker's Contact Info: sottile(at-sign)math.umass.edu


Return to seminar home page

Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

Page loaded on October 02, 2001 at 10:08 PM. Copyright © 1998-99, Sara C. Billey. All rights reserved.