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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DOI: 10.5802/alco.28
Classification: 16T30,  05E05,  05A18
Keywords: Noncommutative symmetric functions, Quasi-symmetric functions, Bell polynomials, Dendriform algebras
Novelli, Jean-Christophe 1; Thibon, Jean-Yves 1; Toumazet, Frédéric 1

1 Laboratoire d’informatique Gaspard-Monge Université Paris-Est Marne-la-Vallée 5, Boulevard Descartes Champs-sur-Marne 77454 Marne-la-Vallée cedex 2 France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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