The Hopf algebra of permutations of Malvenuto and Reutenauer

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AMS 2002 National Meeting in San Diego, CA
6-9 January, 2002

Title: The Hopf algebra of permutations of Malvenuto and Reutenauer.
Session Name:AMS Special Session on Algebraic Combinatorics

Author: Marcelo Aguiar
Author: Frank Sottile

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.