SIAM Journal on Mathematical Analysis - Special issue: the articles in this issue are dedicated to Richard Askey and Frank Olver
A “Fourier Transform” for Multiplicative Functionson Non-Crossing Partitions
Journal of Algebraic Combinatorics: An International Journal
Discrete Mathematics
On the combinatorics of cumulants
Journal of Combinatorial Theory Series A
An umbral setting for cumulants and factorial moments
European Journal of Combinatorics
Explicit formulae for Kerov polynomials
Journal of Algebraic Combinatorics: An International Journal
On a symbolic representation of non-central Wishart random matrices with applications
Journal of Multivariate Analysis
Hi-index | 0.00 |
We provide a unifying polynomial expression giving moments in terms of cumulants, and vice versa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show that in the free cumulant theory the volume polynomial of Pitman and Stanley plays the role of the complete Bell exponential polynomial in the classical theory. Moreover, via generalized Abel polynomials we construct a new class of cumulants, including the classical, boolean and free ones, and the convolutions linearized by them. Finally, via an umbral Fourier transform, we state an explicit connection between boolean and free convolution.