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

N. Bergeron, C. Hohlweg, M. Rosas, M. Zabrocki
2006 Electronic Journal of Combinatorics  
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.
doi:10.37236/1101 fatcat:s7qk2hkykjg5jbvqh5madtj5ka