Article PDF
References
Bercovici, H., Voiculescu, D.: Free convolution of measures with unbounded support. PAM-572 (Preprint 1992)
Bonin, J., Shapiro, L., Simion, R.: Someq-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths. (Preprint 1991)
Bourbaki, N.: Elements of mathematics; Algebra I. Berlin Heidelberg New York: Springer 1988
Comtet, L.: Advanced combinatorics. Dordrecht: Reidel 1974
Edelman, P.H.: Chain enumeration and non-crossing partitions. Discrete Math.31, 171–180 (1980)
Edelman, P.H.: Multichains, non-crossing partitions and trees. Discrete Math.40, 171–179 (1982)
Edelman, P.H., Simion, R.: Chains in the lattice of non-crossing partitions. (Preprint 1991)
Glockner, P., Schürmann, M., Speicher, R.: Realization of free white noises. Arch. Math.58, 407–416 (1992)
Hilton, P., Pederson, J.: Catalan numbers, their generalization, and their uses. Math. Intell.13 (no. 2), 64–75 (1991)
Klarner, D.A.: Correspondences between plane trees and binary sequences. J. Comb. Theory9, 401–411 (1970)
Kreweras, G.: Sur les partitions non croisées d'un cycle. Discrete Math.1, 333–350 (1972)
Maassen, H.: Addition of freely independent random variables. J.Funct. Anal.106, 409–438 (1992)
Polya, G., Szegö, G.: Aufgaben und Lehrsätze aus der Analysis I. Berlin Heidelberg New York: Springer 1954
Poupard, Y.: Etude et denombrement paralleles des partitions non croisées d'un cycle et des coupage d'un polygone convexe. Discrete Math.2, 279–288 (1972)
Rota, G.-C.: On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheor. Verw. Geb.2, 340–368 (1964)
Rota, G.-C.: Finite operator calculus. New York: Academic Press 1975
Shiryayev, A.N.: Probability. (Grad. Texts Math., vol. 95) Berlin Heidelberg New York: Springer 1984
Simion, R.: Combinatorial statistics on non-crossing partitions. (Preprint 1991)
Simion, R., Ullman, D.: On the structure of the lattice of noncrossing partitions. Discrete Math.98, 193–206 (1991)
Speicher, R.: A new example of ‘Independence’ and ‘White Noise’. Probab. Theory Relat. Fields84, 141–159 (1990)
Speicher, R.: The lattice of admissible partitions In: Accardi, L. (ed.) Quantum probability and related topics, vol. VIII. Singapore: World Scientific (to appear)
Speicher, R.: Free convolution and the random sum of matrices. (Publ., Res. Inst. Math. Sci., vol. 29) (to appear)
Voiculescu, D.: Symmetries of some reduced free productC*-algebras. In: Araki, H., Moore, C.C., Stratila, S., Voiculescu, D. (eds.) Operator algebras and their connection with topology and ergodic theory (Lect. Notes Math., vol. 1132, pp. 556–588) Berlin Heidelberg New York: Springer 1985
Voiculescu, D.: Addition of certain non-commuting random variables. J. Funct. Anal.66, 323–346 (1986)
Voiculescu, D.: Limit laws for random matrices and free products. Invent. Math.104, 201–220 (1991)
Author information
Authors and Affiliations
Additional information
This work has been supported by the Deutsche Forschungsgemeinschaft (SFB 123)
Rights and permissions
About this article
Cite this article
Speicher, R. Multiplicative functions on the lattice of non-crossing partitions and free convolution. Math. Ann. 298, 611–628 (1994). https://doi.org/10.1007/BF01459754
Received:
Issue date:
DOI: https://doi.org/10.1007/BF01459754
