2001/10/02 by Franz Lehner
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Random Matrices and Applications #math.CO #msc:05A18 #msc:05A19 #msc:46L54
paper · pdf · doi:10.1006/eujc.2002.0619
published as European J. Combin. 23 (2002), no. 8, 1025--1031 · 7 pages, AMSLaTeX
arxiv created 2001/10/02 · openalex publication_date 2002/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02
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.