Title: Δ-cumulants in terms of moments,
Abstract: The \Delta-convolution of real probability measures, introduced by Bożejko,
generalizes both free and boolean convolutions. It is linearized by the
\Delta-cumulants, and Yoshida gave a combinatorial formula for moments in terms
of \Delta-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 \Delta-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.