Résumé : The combinatorial solution to an autonomous differential equation y´=φ(y) was shown to be the family of increasing φ-enriched trees (Leroux-Viennot). We introduce a generalization of this kind of differential equations that uses the operation of shift-plethysm instead of usual substitution. Its solution is again a family of φ-enriched trees with labels that give information related to the length of each branch.
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