Symmetric partitions and pairings

Ferenc Oravecz

Colloquium Mathematicae (2000)

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

Abstract

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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.

How to cite

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Oravecz, 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

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  1. [1] N. I. Akhiezer, Classical Moment Problem, Gos. Izdat. Fiz.-Mat. Liter., Moscow, 1961 (in Russian). Zbl0124.06202
  2. [2] G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976. Zbl0371.10001
  3. [3] F. Hiai and D. Petz, The semi-circle law, free random variables and entropy, preprint. Zbl0955.46037
  4. [4] G. Kreweras, Sur les partitions non-croisées d'un cycle, Discrete Math. 1 (1972), 333-350. Zbl0231.05014
  5. [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. [6] J. Touchard, Sur un problème de configurations et sur les fractions continues, Canad. J. Math. 4 (1952), 2-25. Zbl0047.01801
  7. [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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