Geodesic
(Pure) Transcendence Bases in φ-Deformed Shuffle Bialgebras
Séminaire lotharingien de combinatoire, Tome 74 (2015-2018) 
Van Chien Bui; Gérard H.E. Duchamp; Quoc Huan Ngô; Vincel Hoang Ngoc Minh; Christophe Tollu. (Pure) Transcendence Bases in φ-Deformed Shuffle Bialgebras. Séminaire lotharingien de combinatoire, Tome 74 (2015-2018). http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a5/
@article{SLC_2015-2018_74_a5,
     author = {Van Chien Bui and G\'erard H.E. Duchamp and Quoc Huan Ng\^o and Vincel Hoang Ngoc Minh and Christophe Tollu},
     title = {(Pure) {Transcendence} {Bases} in {\ensuremath{\varphi}-Deformed} {Shuffle} {Bialgebras}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2015-2018},
     volume = {74},
     url = {http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a5/}
}
TY  - JOUR
AU  - Van Chien Bui
AU  - Gérard H.E. Duchamp
AU  - Quoc Huan Ngô
AU  - Vincel Hoang Ngoc Minh
AU  - Christophe Tollu
TI  - (Pure) Transcendence Bases in φ-Deformed Shuffle Bialgebras
JO  - Séminaire lotharingien de combinatoire
PY  - 2015-2018
VL  - 74
UR  - http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a5/
ID  - SLC_2015-2018_74_a5
ER  - 
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%A Gérard H.E. Duchamp
%A Quoc Huan Ngô
%A Vincel Hoang Ngoc Minh
%A Christophe Tollu
%T (Pure) Transcendence Bases in φ-Deformed Shuffle Bialgebras
%J Séminaire lotharingien de combinatoire
%D 2015-2018
%V 74
%U http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a5/
%F SLC_2015-2018_74_a5

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

Computations with integro-differential operators are often carried out in an associative algebra with unit, and they are essentially non-commutative computations. By adjoining a cocommutative co-product, one can have those operators act on a bialgebra isomorphic to an enveloping algebra. This gives an adequate framework for a computer-algebra implementation via monoidal factorization, (pure) transcendence bases and Poincaré-Birkhoff-Witt bases.

In this paper, we systematically study these deformations, obtaining necessary and sufficient conditions for the operators to exist, and we give the most general cocommutative deformations of the shuffle co-product and an effective construction of pairs of bases in duality. The paper ends by the combinatorial setting of local systems of coordinates on the group of group-like series.