A. L. Yakymiv
On the distribution of the mth maximal cycle lengths of random A-permutations
Let Sn
be the symmetric group of all permutations of degree n, A be some subset of the set of natural numbers
N
, and Tn = Tn
(A) be the set of all permutations of Sn
with cycle lengths belonging to A. The permutations of Tn
are called A-permutations. We consider a wide class of the sets A with the asymptotic density σ > 0. In this article, the limit distributions are obtained for μm
(n)/n
as n → ∞ and m ∈
N
is fixed. Here μm
(n) is the length of the mth maximal cycle in a random permutation uniformly distributed on Tn
. It is shown here that these limit distributions coincide with the limit distributions of the corresponding functionals of the random permutations in the Ewens model with parameter σ.
Discrete Mathematics and Applications, Walter de Gruyter
Print ISSN: 0924-9266
Volume: 15, 10/2005
Seiten: 527 - 546
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