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math.CO2001
Free cumulants and enumeration of connected partitions
Franz Lehner
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 class…
math.CO2001
Cumulants, lattice paths, and orthogonal polynomials
Franz Lehner
A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions a…