Journal of Algebraic Combinatorics

, Volume 6, Issue 2, pp 141-160

First online:

A “Fourier Transform” for Multiplicative Functions on Non-Crossing Partitions

  • Alexandru NicaAffiliated withDepartment of Mathematics, University of Michigan
  • , Roland SpeicherAffiliated withInstitut für Angewandte Mathematik, Universität Heidelberg

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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

non-crossing partition Moebius function free random variables