Combinatorics of Free Cumulants

Journal of Combinatorial Theory. Series A

Volumn 90, Issue 2, 2000, Pages 267-292

  Krawczyk, Bernadette ^a   Speicher, Roland ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008293104     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.1999.3032     Document Type: Article

References (18)

1. P. Edelman, Chain enumeration and non-crossing partitions, Discrete Math. 31 (1980), 171-180.
2. U. Haagerup and F. Larsen, Brown's spectral distribution measure for R-diagonal elements in finite von Neumann algebras, preprint, 1999.
3. B. Krawczyk, "Charakterisierung von R-diagonalen Zufallsvariablen," Diplomarbeit, Universität Heidelberg, 1998.
4. G. Kreweras, Sur les partitions non croisées d'un cycle, Discrete Math. 1 (1972), 333-350.
5. F. Larsen, Powers of R-diagonal elements, preprint, 1999.
6. A. Nica, R-transforms of free joint distributions and non-crossing partitions, J. Funct. Anal. 135 (1996), 271-296.
7. A. Nica and R. Speicher, On the multiplication of free n-tuples of noncommutative random variables, Amer. J. Math. 118 (1996), 799-837.
8. A. Nica and R. Speicher, R-diagonal pairs - A common approach to Haar unitaries and circular elements, in "Fields Institute Communications," Vol. 12, pp. 149-188, Amer. Math. Soc., Providence, 1997.
9. A. Nica and R. Speicher, Commutators of free random variables, Duke Math. J. 92 (1998), 553-592.
10. A. Nica, D. Shlyakhtenko, and R. Speicher, R-diagonal elements and freeness with amalgamation, preprint, 1999.
11. F. Oravecz, On the powers of Voiculescu's circular element, preprint, 1998.
12. R. Simion and D. Ullman, On the structure of the lattice of noncrossing partitions, Discrete Math. 98 (1991), 193-206.
13. D. Shlyakhtenko, Free quasi-free states, Pacific J. Math. 177 (1997), 329-368.
14. R. Speicher, Multiplicative functions on the lattice of non-crossing partitions and free convolution, Math. Ann. 298 (1994), 611-628.
15. R. Speicher, Free probability theory and non-crossing partitions, in "Seminaire Loth. Comb. B39c, 1997."
16. R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability, Mem. Amer. Math. Soc. 132 (1998), x + 88.
17. D. Voiculescu (Ed.), "Free Probability Theory," Fields Institute Communications, Vol. 12, Amer. Math. Soc., Providence, 1997.
18. D. Voiculescu, K. Dykema, and A. Nica, "Free Random Variables," CRM Monogr. Ser., Vol. 1, Amer. Math. Soc., Providence, 1992.