Grammaire de Ramanujan et Arbres de Cayley

Dominique Dumont, Armand Ramamonjisoa


We study three sequences of polynomials defined as successive derivatives with respect to a differential operator associated with a grammar (one of these sequences was originally introduced by Ramanujan). Combinatorial interpretations for these polynomials are found in terms of rooted trees and graphs of mappings from $[n]$ to $[n]$.

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