∆-cumulants in terms of moments
Résumé
The ∆-convolution of real probability measures, introduced by Bo˙ zejko, generalizes both free and boolean convolutions. It is linearized by the ∆-cumulants, and Yoshida gave a combinatorial formula for moments in terms of ∆-cumulants, that implicitly defines the latter. It relies on the definition of an appropriate weight on noncrossing partitions. We give here two different expressions for the ∆-cumulants: the first one is a simple variant of Lagrange inversion formula, and the second one is a combinatorial inversion of Yoshida's formula involving Schröder trees.
Domaines
Combinatoire [math.CO]
Origine : Fichiers produits par l'(les) auteur(s)
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