Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables
Bergeron, Nantel · Hohlweg, Christophe · Rosas, Mercedes · Zabrocki, Mike
Original · EN
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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