Dérivées directionnelles et développements de Taylor combinatoires. (Directional derivatives and combinatorial Taylor expansions) (Q753815)

Let U be the set of all isomorphism classes of atomic species, K be a binomial half-ring. The author studies two new notions: (a) the combinatorial directional derivative of a K-species in the direction of another K-species and, (b) the Taylor expansions in the extension of the half-ring K(X) of all formal power series in one indeterminate X. Certain similarities and differences between the two notions are shown.