Symmetric partitions and pairings

• Autorzy: Ferenc Oravecz
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 86
• Numer: 1
• Strony: 93-101

Daty

wydano

2000

otrzymano

1998-10-13

poprawiono

1999-09-12

Twórcy

autor

Ferenc Oravecz

• Rényi Alfréd Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1053 Budapest, Hungary

Bibliografia

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