Free cumulants and enumeration of connected partitions

Details Free cumulants and enumeration of connected partitions Free cumulants and enumeration of connected partitions

2001-10-02

arxiv.org/abs/math/0110030v1

European J. Combin. 23 (2002), no. 8, 1025--1031

Mathematics

Combinatorics

7 pages, AMSLaTeX

Scientific paper

10.1006/eujc.2002.0619

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.

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