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)
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This work has been supported by the Deutsche Forschungsgemeinschaft (SFB 123)
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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
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DOI: https://doi.org/10.1007/BF01459754