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.
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
@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/}
}
TY - JOUR AU - N. Bergeron AU - C. Hohlweg AU - M. Rosas AU - M. Zabrocki TI - Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables JO - The electronic journal of combinatorics PY - 2006 VL - 13 UR - http://geodesic.mathdoc.fr/articles/10.37236/1101/ DO - 10.37236/1101 ID - 10_37236_1101 ER -
%0 Journal Article %A N. Bergeron %A C. Hohlweg %A M. Rosas %A M. Zabrocki %T Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables %J The electronic journal of combinatorics %D 2006 %V 13 %U http://geodesic.mathdoc.fr/articles/10.37236/1101/ %R 10.37236/1101 %F 10_37236_1101
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