Journal of Algebraic Combinatorics

, Volume 6, Issue 2, pp 141–160

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


  • Alexandru Nica
    • Department of MathematicsUniversity of Michigan
  • Roland Speicher
    • Institut für Angewandte MathematikUniversität Heidelberg

DOI: 10.1023/A:1008643104945

Cite this article as:
Nica, A. & Speicher, R. Journal of Algebraic Combinatorics (1997) 6: 141. doi:10.1023/A:1008643104945


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 partitionMoebius functionfree random variables

Copyright information

© Kluwer Academic Publishers 1997