Noncommutative Bell polynomials and the dual immaculate basis
Combinatorics
2020-03-23 v4
Abstract
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 [Canad. J. Math. 69 (2017), 21--53], and interpret them in terms of the tridendriform structure of WQSym. We then present a variant of Rey's self-dual Hopf algebra of set partitions [FPSAC'07, Tianjin] adapted to our noncommutative Bell polynomials and give a complete description of the Bell equivalence classes as linear extensions of explicit posets.
Cite
@article{arxiv.1705.08113,
title = {Noncommutative Bell polynomials and the dual immaculate basis},
author = {Jean-Christophe Novelli and Jean-Yves Thibon and Frédéric Toumazet},
journal= {arXiv preprint arXiv:1705.08113},
year = {2020}
}
Comments
27 pages