The asymptotic normality of the number of congruent cycles in a random permutation. (English. Russian original) Zbl 1266.60044
Discrete Math. Appl. 22, No. 1, 91-100 (2012); translation from Diskretn. Mat. 24, No. 1, 123-131 (2012).
Summary: In the context of a \(d\)-dimensional parametric model of random \(n\)-permutations, we establish the joint asymptotic, as \(n\to \infty \), normality of the numbers of congruent cycles in a random permutation. On this basis, we suggest a new statistical test for the hypothesis of equiprobability of permutations.
MSC:
| 60F05 | Central limit and other weak theorems |
| 05A05 | Permutations, words, matrices |
| 60C05 | Combinatorial probability |
| 62G20 | Asymptotic properties of nonparametric inference |
