We define a new family of noncommutative Bell polynomials in the algebra of free quasi-symmetric functions and relate it to the dual immaculate basis of quasi-symmetric functions. We obtain noncommutative versions of Grinberg’s results [], and interpret these in terms of the tridendriform structure of . We then present a variant of Rey’s self-dual Hopf algebra of set partitions [] adapted to our noncommutative Bell polynomials and give a complete description of the Bell equivalence classes as linear extensions of explicit posets.
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Accepted:
Published online:
DOI: 10.5802/alco.28
Keywords: Noncommutative symmetric functions, Quasi-symmetric functions, Bell polynomials, Dendriform algebras
Novelli, Jean-Christophe 1; Thibon, Jean-Yves 1; Toumazet, Frédéric 1
CC-BY 4.0
@article{ALCO_2018__1_5_653_0,
author = {Novelli, Jean-Christophe and Thibon, Jean-Yves and Toumazet, Fr\'ed\'eric},
title = {Noncommutative {Bell} polynomials and the dual immaculate basis},
journal = {Algebraic Combinatorics},
pages = {653--676},
publisher = {MathOA foundation},
volume = {1},
number = {5},
year = {2018},
doi = {10.5802/alco.28},
mrnumber = {3887406},
zbl = {06987761},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.28/}
}
TY - JOUR AU - Novelli, Jean-Christophe AU - Thibon, Jean-Yves AU - Toumazet, Frédéric TI - Noncommutative Bell polynomials and the dual immaculate basis JO - Algebraic Combinatorics PY - 2018 SP - 653 EP - 676 VL - 1 IS - 5 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.28/ DO - 10.5802/alco.28 LA - en ID - ALCO_2018__1_5_653_0 ER -
%0 Journal Article %A Novelli, Jean-Christophe %A Thibon, Jean-Yves %A Toumazet, Frédéric %T Noncommutative Bell polynomials and the dual immaculate basis %J Algebraic Combinatorics %D 2018 %P 653-676 %V 1 %N 5 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.28/ %R 10.5802/alco.28 %G en %F ALCO_2018__1_5_653_0
Novelli, Jean-Christophe; Thibon, Jean-Yves; Toumazet, Frédéric. Noncommutative Bell polynomials and the dual immaculate basis. Algebraic Combinatorics, Volume 1 (2018) no. 5, pp. 653-676. doi : 10.5802/alco.28. https://alco.centre-mersenne.org/articles/10.5802/alco.28/
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