Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables

Details Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables

2005-06-17

arxiv.org/abs/math/0506360v1

Electron. J. Combin. 13 (2006), no. 1, Research Paper 75, 19 pp.

Mathematics

Combinatorics

17 pages

Scientific paper

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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