Geodesic
Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables
The electronic journal of combinatorics, Tome 13 (2006)
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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
Classification : 05E05, 05E10, 16G10, 20C08
Mots-clés : Schur function 
@article{10_37236_1101,
     author = {N. Bergeron and C. Hohlweg and M. Rosas and M. Zabrocki},
     title = {Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1101},
     zbl = {1098.05079},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1101/}
}
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N. Bergeron; C. Hohlweg; M. Rosas; M. Zabrocki. Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1101

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