ALGEBRAIC COMBINATORICS

no. 5

Noncommutative Bell polynomials and the dual immaculate basis
Algebraic Combinatorics, Volume 1 (2018) no. 5, pp. 653-676.

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 WQSym. 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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Published online:
DOI: https://doi.org/10.5802/alco.28
Classification: 16T30,  05E05,  05A18
Keywords: Noncommutative symmetric functions, Quasi-symmetric functions, Bell polynomials, Dendriform algebras 
@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},
     zbl = {06987761},
     mrnumber = {3887406},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.28/}
}
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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