# Symmetric partitions and pairings

Colloquium Mathematicae (2000)

- Volume: 86, Issue: 1, page 93-101
- ISSN: 0010-1354

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topOravecz, Ferenc. "Symmetric partitions and pairings." Colloquium Mathematicae 86.1 (2000): 93-101. <http://eudml.org/doc/210843>.

@article{Oravecz2000,

abstract = {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.},

author = {Oravecz, Ferenc},

journal = {Colloquium Mathematicae},

keywords = {partitions; moment sequence; distribution},

language = {eng},

number = {1},

pages = {93-101},

title = {Symmetric partitions and pairings},

url = {http://eudml.org/doc/210843},

volume = {86},

year = {2000},

}

TY - JOUR

AU - Oravecz, Ferenc

TI - Symmetric partitions and pairings

JO - Colloquium Mathematicae

PY - 2000

VL - 86

IS - 1

SP - 93

EP - 101

AB - 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.

LA - eng

KW - partitions; moment sequence; distribution

UR - http://eudml.org/doc/210843

ER -

## References

top- [1] N. I. Akhiezer, Classical Moment Problem, Gos. Izdat. Fiz.-Mat. Liter., Moscow, 1961 (in Russian). Zbl0124.06202
- [2] G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976. Zbl0371.10001
- [3] F. Hiai and D. Petz, The semi-circle law, free random variables and entropy, preprint. Zbl0955.46037
- [4] G. Kreweras, Sur les partitions non-croisées d'un cycle, Discrete Math. 1 (1972), 333-350. Zbl0231.05014
- [5] F. Oravecz and D. Petz, On the eigenvalue distribution of some symmetric random matrices, Acta Sci. Math. (Szeged) 63 (1997), 383-395. Zbl0889.15006
- [6] J. Touchard, Sur un problème de configurations et sur les fractions continues, Canad. J. Math. 4 (1952), 2-25. Zbl0047.01801
- [7] D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, CRM Monogr. Ser. 1, Amer. Math. Soc., Providence, RI, 1992.

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