Free Cumulants and Enumeration of Connected Partitions |
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Authors: | Franz Lehner |
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Institution: | Institut für Mathematik C, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austriaf1 |
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Abstract: | A combinatorial formula is derived which expresses free cumulants in terms of classical cumulants. 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 partitions, respectively. The proof relies on Möbius inversion on the partition lattice. |
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