Free cumulants and enumeration of connected partitions
Combinatorics
2007-05-23 v1
Abstract
A combinatorial formula is derived which expresses free cumulants in terms of classical comulants. As a corollary, we give a combinatorial interpretation of free cumulants of classical distributions, notably Gaussian and Poisson distributions. The latter count connected pairings and connected set partitions respectively. The proof relies on Moebius inversion on the partition lattice.
Keywords
Cite
@article{arxiv.math/0110030,
title = {Free cumulants and enumeration of connected partitions},
author = {Franz Lehner},
journal= {arXiv preprint arXiv:math/0110030},
year = {2007}
}
Comments
7 pages, AMSLaTeX