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

  • N. Bergeron
  • C. Hohlweg
  • M. Rosas
  • M. Zabrocki


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.

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