2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72974In this paper we investigate the class of invariant positive definite kernels on the free semigroup on N generators. We provide a combinatorial description of the positivity of the kernel in terms of Dyck paths and then we find a displacement equation that encodes the invariance property of the kernel.19 pages, 5 figuresFunctional AnalysisCombinatorics15A69, 47A57text