The Malvenuto-Reutenauer Hopf Algebra of Permutations

Frank Sottile

University of Massachusetts, Amherst

October 24,
refreshments at 3:45pm


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)

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

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