Dérivées directionnelles et développements de Taylor combinatoires
Séminaire lotharingien de combinatoire, Tome 17 (1987)
Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website
Let A be the set of all isomorphism classes of atomic species, let K be a binomial half-ring and K- its rational closure. The differential half-ring K[[A]] of all K-species in the sense of Yeh is a combinatorial and algebraic extension of the half-ring K[[X]] of all formal power series in one indeterminate X. Using the operation of substitution in K[[A]] and the Q-species X^ of "pseudo-singletons" we study two new notions: the combinatorial directional derivative of a K-species in the direction of another K-species and Taylor expansions in K[[A]]. The use of K--species is essential here. We show, along the way, certain similarities and differences between these new notions and their classical analogues in K[[X]]. Tables are given for small cardinalities.
The paper has been finally published under the same title in Discrete Math. 79 (1990), 279-297.
@article{SLC_1987_17_a2,
author = {Gilbert Labelle},
title = {D\'eriv\'ees directionnelles et d\'eveloppements de {Taylor} combinatoires},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {17},
year = {1987},
url = {http://geodesic.mathdoc.fr/item/SLC_1987_17_a2/}
}
Gilbert Labelle. Dérivées directionnelles et développements de Taylor combinatoires. Séminaire lotharingien de combinatoire, Tome 17 (1987). http://geodesic.mathdoc.fr/item/SLC_1987_17_a2/