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On the powers of Voiculescu's circular element

100%

Oravecz F.

Studia Mathematica

2001

tom 145

nr 1

85-95

The main result of the paper is that for a circular element c in a C*-probability space, $(cⁿ,c^{n*})$ is an R-diagonal pair in the sense of Nica and Speicher for every n = 1,2,... The coefficients of the R-series are found to be the generalized Catalan numbers of parameter n-1.

Symmetric partitions and pairings

100%

Oravecz F.

Colloquium Mathematicum

2000

tom 86

nr 1

93-101

The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Oravecz F.

1 2001

1 2000

Wyniki wyszukiwania

On the powers of Voiculescu's circular element

Symmetric partitions and pairings