Grothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables

We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative variables which would be an analogue of the Schur function basis for this bialgebra.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Nantel Bergeron, Christophe Hohlweg, Mercedes Rosas, Mike Zabrocki
• Keywords: COMBINATORICS 2006, Noncommutative Variables, Schur Function Basis, Symmetric Functions