Geodesic
Word Bell Polynomials
Séminaire lotharingien de combinatoire, Tome 75 (2016-2019)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Multivariate partial Bell polynomials have been defined by E.T. Bell in 1934. These polynomials have numerous applications in Combinatorics, Analysis, Algebra, Probabilities, etc. Many of the formulas on Bell polynomials involve combinatorial objects (set partitions, set partitions into lists, permutations, etc.). So it seems natural to investigate analogous formulas in some combinatorial Hopf algebras with bases indexed by these objects. In this paper we investigate the connections between Bell polynomials and several combinatorial Hopf algebras: the Hopf algebra of symmetric functions, the Faà di Bruno algebra, the Hopf algebra of word symmetric functions, etc. We show that Bell polynomials can be defined in all these algebras, and we give analogs of classical results. To this aim, we construct and study a family of combinatorial Hopf algebras whose bases are indexed by colored set partitions. 

@article{SLC_2016-2019_75_a7,
     author = {Ammar Amoud and Jean-Paul Bultel and Ali Chouria and Jean-Gabriel Luque and Olivier Mallet},
     title = {Word {Bell} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {75},
     year = {2016-2019},
     url = {http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a7/}
}
TY  - JOUR
AU  - Ammar Amoud
AU  - Jean-Paul Bultel
AU  - Ali Chouria
AU  - Jean-Gabriel Luque
AU  - Olivier Mallet
TI  - Word Bell Polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 2016-2019
VL  - 75
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a7/
ID  - SLC_2016-2019_75_a7
ER  - 
%0 Journal Article
%A Ammar Amoud
%A Jean-Paul Bultel
%A Ali Chouria
%A Jean-Gabriel Luque
%A Olivier Mallet
%T Word Bell Polynomials
%J Séminaire lotharingien de combinatoire
%D 2016-2019
%V 75
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a7/
%F SLC_2016-2019_75_a7
Ammar Amoud; Jean-Paul Bultel; Ali Chouria; Jean-Gabriel Luque; Olivier Mallet. Word Bell Polynomials. Séminaire lotharingien de combinatoire, Tome 75 (2016-2019). http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a7/