Abstract
We describe the structure of the group of normalized multiplicative functions on lattices of non-crossing partitions. As an application, we give a combinatorial proof of a theorem of D. Voiculescu concerning the multiplication of free random variables
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Nica, A., Speicher, R. A “Fourier Transform” for Multiplicative Functions on Non-Crossing Partitions. Journal of Algebraic Combinatorics 6, 141–160 (1997). https://doi.org/10.1023/A:1008643104945
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DOI: https://doi.org/10.1023/A:1008643104945